!===================================================================================================================120 !===================================================================================================================120 !================================================= Definitions ===================================================120 !===================================================================================================================120 !===================================================================================================================120 ! Jordan Canonical Form (jcf) of the Runge-Kutta A-matrix ! => a = s.jcf.sinv ! Orthogonal Schur decomposition of the Runge-Kutta A-matrix ! => a = Q.T.Q^T ; Q.Q^T = I and T upper triangular with eigenvalues on diagonal ! ! Studies in SIRK paper required 128-bit arithematic ! ! integer, parameter :: wp = 8 ! ! Included schemes ! ! case = 324L3SA ! case = 325L3SA ! case = 435L3SA ! case = 435L3SADAE ! case = 545L3SA ! ! case = 436L4SA ! case = 546L4SA ! case = 547L4SA ! case = 657L4SA ! case = 658L4SA ! ! case = 547L5SA !===================================================================================================================120 !===================================================================================================================120 !=============================================== New Schemes =======================================================120 !===================================================================================================================120 !===================================================================================================================120 ! !===================================================================================================================120 !===================================================================================================================120 ! ********************* SIRK3(2)4L[3]SA ********************* !===================================================================================================================120 !===================================================================================================================120 ! ! SIRK, 4-stage, order =3, stage-order = 3, ! Stiffly-accurate, internally L-stable on ALL stages ! ! D = 2.73853 ! Min{a,b} = {-2.73853, -2.10733} ! Max{a,b} = {2.52989, 2.1666} ! {Min.,Max} Eig(M), = {-0.258772, 15.6886} ! Cmeasure = 0.195656 ! {Min., Max., RMS} Eig(M)int = {-0.391399, -0.220775, 0.544784} ! Condition Number of S, kappaI(S)_{2,Inf} = {140.364, 217.728} ! ! 31 29 83 ! c = {--, --, --, 1} ! 79 56 94 ! ! g = 0.224 ! ! {A1,A2,A3,A4,A5,A6,A7} = {0, 0, 0, 0.0014593162, 0.011812760, 0.029047429, 0.048636437} ! Embedded method ! {A1,A2,A3,A4,A5,A6,A7} = {0, 0, 0.0029788168, 0.0050784205, 0.0036531995, 0.020282487, 0.039741875} ! B,C,E = {1.70484, 2.19474, 0.489898} !============================================================== !===================================================================================================================120 casename='SIRK3[2]4L[3]SA' ! SIRK3(2)4L[3]SA !===================================================================================================================120 ns = 4 aI(1,1) = 4783396728397957.0_wp/2266523577527685.0_wp aI(2,1) = 2326913609352083.0_wp/946022760872741.0_wp aI(3,1) = 1967360629700260.0_wp/777646236567989.0_wp aI(4,1) = 2826975679162216.0_wp/1304799141207799.0_wp aI(1,2) = -2647563713972094.0_wp/1144006995361037.0_wp aI(2,2) = -2464293013905623.0_wp/899859900855167.0_wp aI(3,2) = -2785931316081475.0_wp/1023888125223952.0_wp aI(4,2) = -9752127902772385.0_wp/4627724292068513.0_wp aI(1,3) = 3210684183084084.0_wp/2522776014286931.0_wp aI(2,3) = 1524146046600233.0_wp/850770634443326.0_wp aI(3,3) = 2406242809268325.0_wp/1051139311357133.0_wp aI(4,3) = 1704164157419377.0_wp/999023358192832.0_wp aI(1,4) = -789724215472725.0_wp/1167472046181577.0_wp aI(2,4) = -2234328056230635.0_wp/2246047124919004.0_wp aI(3,4) = -996035411241107.0_wp/819677381399927.0_wp aI(4,4) = -15977473228921.0_wp/20882812500000.0_wp ! ======= bE(1) = 2826975679162216.0_wp/1304799141207799.0_wp bE(2) = -9752127902772385.0_wp/4627724292068513.0_wp bE(3) = 1704164157419377.0_wp/999023358192832.0_wp bE(4) = -15977473228921.0_wp/20882812500000.0_wp ! ======= bEh(1) = 2324884253982426.0_wp/1089322965426587.0_wp bEh(2) = -1323224273690905.0_wp/652278104980391.0_wp bEh(3) = 3590104309545367.0_wp/2316912895809890.0_wp bEh(4) = -171016611865999.0_wp/261035156250000.0_wp ! ======= cE(1) = 31.0_wp/79.0_wp cE(2) = 29.0_wp/56.0_wp cE(3) = 83.0_wp/94.0_wp cE(4) = 1.0_wp/1.0_wp ! ======= g = 28.0_wp/125.0_wp ! ======= s(1,1) = -71196351214.0_wp/21699077799125.0_wp s(2,1) = 511252967.0_wp/3864506912000.0_wp s(3,1) = 248721088433.0_wp/18277364300500.0_wp s(4,1) = 2.0_wp/125.0_wp s(1,2) = 5043911297012.0_wp/410788420469559.0_wp s(2,2) = 24746127117259.0_wp/952859084753925.0_wp s(3,2) = 17187610276169.0_wp/523607440739176.0_wp s(4,2) = 3.0_wp/250.0_wp s(1,3) = -36932809119951.0_wp/378173792501897.0_wp s(2,3) = -20586398313523.0_wp/444477710727195.0_wp s(3,3) = 48231227690022.0_wp/1619014344230629.0_wp s(4,3) = -19.0_wp/250.0_wp s(1,4) = -986437687460059.0_wp/1335674949507600.0_wp s(2,4) = -238430756116351.0_wp/926403730007661.0_wp s(3,4) = 1844381570819505.0_wp/6861973934298641.0_wp s(4,4) = -529.0_wp/1000.0_wp ! ======= sinv(1,1) = -22076546643153719.0_wp/1159206183666295.0_wp sinv(2,1) = 19272419784616935.0_wp/695215711093199.0_wp sinv(3,1) = 7944355542530571.0_wp/105423923786671.0_wp sinv(4,1) = -5296579378393091.0_wp/491634555930342.0_wp sinv(1,2) = -35384508360177623.0_wp/1194593617841934.0_wp sinv(2,2) = -5745975330224781.0_wp/1317268291319180.0_wp sinv(3,2) = -73052969117086637.0_wp/792317665267484.0_wp sinv(4,2) = 33559690771529329.0_wp/2739228554481876.0_wp sinv(1,3) = 14176504530641337.0_wp/1079584537866442.0_wp sinv(2,3) = 21714593573089403.0_wp/697432006338939.0_wp sinv(3,3) = 116038719449804916.0_wp/2059151598092045.0_wp sinv(4,3) = -4133589617046078.0_wp/591138574609943.0_wp sinv(1,4) = 55452239201816201.0_wp/1163225831554744.0_wp sinv(2,4) = -24672098473409517.0_wp/1188454078415299.0_wp sinv(3,4) = -55034091063782696.0_wp/1735379099761881.0_wp sinv(4,4) = 6328689904686437.0_wp/1740234375000000.0_wp ! ======= jcf(1,1) = 28.0_wp/125.0_wp jcf(2,1) = 0.0_wp/1.0_wp jcf(3,1) = 0.0_wp/1.0_wp jcf(4,1) = 0.0_wp/1.0_wp jcf(1,2) = 1.0_wp/1.0_wp jcf(2,2) = 28.0_wp/125.0_wp jcf(3,2) = 0.0_wp/1.0_wp jcf(4,2) = 0.0_wp/1.0_wp jcf(1,3) = 0.0_wp/1.0_wp jcf(2,3) = 1.0_wp/1.0_wp jcf(3,3) = 28.0_wp/125.0_wp jcf(4,3) = 0.0_wp/1.0_wp jcf(1,4) = 0.0_wp/1.0_wp jcf(2,4) = 0.0_wp/1.0_wp jcf(3,4) = 1.0_wp/1.0_wp jcf(4,4) = 28.0_wp/125.0_wp ! ======= q(1,1) = 181360744760415.0_wp/1175111503405571.0_wp q(1,2) = -142924022700197.0_wp/302962827868093.0_wp q(1,3) = -517696269002069.0_wp/818469907343958.0_wp q(1,4) = -1284231596709874.0_wp/2159819943522249.0_wp q(2,1) = -6357283204524.0_wp/1021602748837585.0_wp q(2,2) = -3138500576575331.0_wp/4293770114851474.0_wp q(2,3) = -220039088991413.0_wp/2391691877105876.0_wp q(2,4) = 57619995479959.0_wp/85213974172446.0_wp q(3,1) = -553865195896066.0_wp/865281226454275.0_wp q(3,2) = -430566631682640.0_wp/1033298936865391.0_wp q(3,3) = 225971083087147.0_wp/436746693251866.0_wp q(3,4) = -349046968300405.0_wp/904426113430298.0_wp q(4,1) = -425928260770080.0_wp/565937824788991.0_wp q(4,2) = 233321695056405.0_wp/884792657642507.0_wp q(4,3) = -267385592005726.0_wp/469923456785049.0_wp q(4,4) = 227813881539195.0_wp/1135014450643228.0_wp ! ======= t(1,1) = 28.0_wp/125.0_wp t(1,2) = 223051071052461.0_wp/370246718881346.0_wp t(1,3) = -549942416813210.0_wp/1204974715247227.0_wp t(1,4) = 3452275249687981.0_wp/689156386452076.0_wp t(2,1) = 0.0_wp/1.0_wp t(2,2) = 28.0_wp/125.0_wp t(2,3) = -277027125905443.0_wp/978852412808415.0_wp t(2,4) = 7703590815907195.0_wp/1367460729487784.0_wp t(3,1) = 0.0_wp/1.0_wp t(3,2) = 0.0_wp/1.0_wp t(3,3) = 28.0_wp/125.0_wp t(3,4) = 3167849117778602.0_wp/1402177958317911.0_wp t(4,1) = 0.0_wp/1.0_wp t(4,2) = 0.0_wp/1.0_wp t(4,3) = 0.0_wp/1.0_wp t(4,4) = 28.0_wp/125.0_wp !===================================================================================================================120 !===================================================================================================================120 ! ********************* SIRK3(2)5L[3]SA ********************* !===================================================================================================================120 !===================================================================================================================120 ! SIRK, 5-stage, order =3, stage-order = 3, ! Stiffly-accurate, internally L-stable on ALL stages ! ! D = 0.898324 ! Min{a,b} = {-0.633397, -0.396585} ! Max{a,b} = {0.898324, 0.81917} ! {Min.,Max} Eig(M), = {-0.0703295, 1.1428} ! Cmeasure = 0.0964971 ! {Min., Max., RMS} Eig(M)int = {-0.0852955, -0.0598509, 0.150142} ! Condition Number of S, kappaI(S)_{2,Inf} = {472.085, 746.127} ! ! 21 32 94 155 ! c = {--, --, ---, ---, 1} ! 82 83 143 182 ! ! g = 0.162 ! ! {A1,A2,A3,A4,A5,A6,A7} = {0, 0, 0, 0.0017320508, 0.0063002824, 0.011490967, 0.015815874} ! Embedded method ! {A1,A2,A3,A4,A5,A6,A7} = {0, 0, 0.0035355339, 0.0043301270, 0.00022294884, 0.0057005402, 0.010670093} ! B,C,E = {1.22474, 1.71464, 0.489898} !============================================================== !===================================================================================================================120 casename='SIRK3[2]5L[3]SA' ! SIRK3(2)5L[3]SA !===================================================================================================================120 ns = 5 aI(1,1) = 1474281924932186.0_wp/1952371688995909.0_wp aI(2,1) = 1022908247984596.0_wp/1138684981116423.0_wp aI(3,1) = 2912697333550337.0_wp/3648586350671507.0_wp aI(4,1) = 222462025861571.0_wp/269023580306671.0_wp aI(5,1) = 1050379369822896.0_wp/1282248443840773.0_wp aI(1,2) = -412958667332915.0_wp/705587397971974.0_wp aI(2,2) = -547865828466157.0_wp/864965008334574.0_wp aI(3,2) = -932594326245055.0_wp/2453898662595723.0_wp aI(4,2) = -66152309156827.0_wp/176528479801661.0_wp aI(5,2) = -282547194442154.0_wp/712449891784871.0_wp aI(1,3) = -17485462680611.0_wp/295612208184605.0_wp aI(2,3) = -48277366024589.0_wp/476358302807563.0_wp aI(3,3) = 81734072021249.0_wp/565326449230152.0_wp aI(4,3) = 1780051060589.0_wp/175648863700746.0_wp aI(5,3) = 107797719578987.0_wp/730701170197158.0_wp aI(1,4) = 102948180578905.0_wp/368387366634381.0_wp aI(2,4) = 813542730710541.0_wp/1804638009268678.0_wp aI(3,4) = 323646391361143.0_wp/1528570816618639.0_wp aI(4,4) = 575403547004867.0_wp/848237090663332.0_wp aI(5,4) = 434143421085421.0_wp/769012162557214.0_wp aI(1,5) = -83309893875091.0_wp/621423359608146.0_wp aI(2,5) = -282861578962254.0_wp/1236038197633837.0_wp aI(3,5) = -137290418070859.0_wp/1171122932455868.0_wp aI(4,5) = -644978865476729.0_wp/2231592498092281.0_wp aI(5,5) = -23231966998411.0_wp/172525877589063.0_wp ! ======= bE(1) = 1050379369822896.0_wp/1282248443840773.0_wp bE(2) = -282547194442154.0_wp/712449891784871.0_wp bE(3) = 107797719578987.0_wp/730701170197158.0_wp bE(4) = 434143421085421.0_wp/769012162557214.0_wp bE(5) = -23231966998411.0_wp/172525877589063.0_wp ! ======= bEh(1) = 629351645271055.0_wp/744047090183874.0_wp bEh(2) = -470917768418927.0_wp/1092008561637032.0_wp bEh(3) = 195791933442169.0_wp/1008363386912982.0_wp bEh(4) = 447483981783011.0_wp/959093320967504.0_wp bEh(5) = -105421987243244.0_wp/1399152155249621.0_wp ! ======= cE(1) = 21.0_wp/82.0_wp cE(2) = 32.0_wp/83.0_wp cE(3) = 94.0_wp/143.0_wp cE(4) = 155.0_wp/182.0_wp cE(5) = 1.0_wp/1.0_wp ! ======= g = 81.0_wp/500.0_wp ! ======= s(1,1) = 4947617479121.0_wp/402261963832407.0_wp s(2,1) = 28405977459276.0_wp/923591804468735.0_wp s(3,1) = -33507583397644.0_wp/807181897954513.0_wp s(4,1) = 227997532048936.0_wp/1226367396934393.0_wp s(5,1) = 163.0_wp/500.0_wp s(1,2) = -43774077070329.0_wp/215363973961673.0_wp s(2,2) = 20766928928131.0_wp/549454922622742.0_wp s(3,2) = 638456857069337.0_wp/857191380778936.0_wp s(4,2) = 519511925564159.0_wp/653304730003900.0_wp s(5,2) = 173.0_wp/1000.0_wp s(1,3) = 2855373315894802.0_wp/1278275491785333.0_wp s(2,3) = 1824762262981909.0_wp/602892120513500.0_wp s(3,3) = -6051500584842199.0_wp/1620416081059294.0_wp s(4,3) = -639364217648389.0_wp/765889164020926.0_wp s(5,3) = -1907.0_wp/1000.0_wp s(1,4) = -14174445211761601.0_wp/1087317058053742.0_wp s(2,4) = -9088233282711589.0_wp/886729779078240.0_wp s(3,4) = -17680669788368191.0_wp/1338480535269308.0_wp s(4,4) = 3284155748225062.0_wp/448712486712991.0_wp s(5,4) = -2127.0_wp/250.0_wp s(1,5) = -13596890301487045.0_wp/1020345742782082.0_wp s(2,5) = 63992215082920793.0_wp/1143105704498715.0_wp s(3,5) = -125500872583515809.0_wp/1011239502242016.0_wp s(4,5) = 38276833896126713.0_wp/1039964864688884.0_wp s(5,5) = -7463.0_wp/100.0_wp ! ======= sinv(1,1) = 351394780605173.0_wp/839358755818999.0_wp sinv(2,1) = 1330777601937318.0_wp/795481432053329.0_wp sinv(3,1) = 490128739567013.0_wp/427307033552416.0_wp sinv(4,1) = 233501657123041.0_wp/1744202466443746.0_wp sinv(5,1) = -32062857674191.0_wp/824990108856467.0_wp sinv(1,2) = -234404024542601.0_wp/1134589678860150.0_wp sinv(2,2) = -1151021210318105.0_wp/1358615503429294.0_wp sinv(3,2) = -683269405163406.0_wp/966875218441607.0_wp sinv(4,2) = -74723612327045.0_wp/534086989691522.0_wp sinv(5,2) = 14283849542969.0_wp/458680795314903.0_wp sinv(1,3) = -865167482940159.0_wp/645257695348499.0_wp sinv(2,3) = 683864965041937.0_wp/1777335767855159.0_wp sinv(3,3) = -139170347162891.0_wp/1120599658865821.0_wp sinv(4,3) = -25220266325317.0_wp/834079063018617.0_wp sinv(5,3) = 1620087511033.0_wp/978565140329230.0_wp sinv(1,4) = 446378501464381.0_wp/527175839021723.0_wp sinv(2,4) = 898096976573123.0_wp/582419892002112.0_wp sinv(3,4) = 423694189511744.0_wp/840714676603289.0_wp sinv(4,4) = 53277083060288.0_wp/683723642873283.0_wp sinv(5,4) = -3216699178902.0_wp/222027911250323.0_wp sinv(1,5) = 2038003262845827.0_wp/842997998931728.0_wp sinv(2,5) = -181413783848725.0_wp/222982568414766.0_wp sinv(3,5) = -699158869087128.0_wp/2498556796577167.0_wp sinv(4,5) = -29108121340183.0_wp/725176615080949.0_wp sinv(5,5) = 35962341561213.0_wp/5136498862334101.0_wp ! ======= jcf(1,1) = 81.0_wp/500.0_wp jcf(2,1) = 0.0_wp/1.0_wp jcf(3,1) = 0.0_wp/1.0_wp jcf(4,1) = 0.0_wp/1.0_wp jcf(5,1) = 0.0_wp/1.0_wp jcf(1,2) = 1.0_wp/1.0_wp jcf(2,2) = 81.0_wp/500.0_wp jcf(3,2) = 0.0_wp/1.0_wp jcf(4,2) = 0.0_wp/1.0_wp jcf(5,2) = 0.0_wp/1.0_wp jcf(1,3) = 0.0_wp/1.0_wp jcf(2,3) = 1.0_wp/1.0_wp jcf(3,3) = 81.0_wp/500.0_wp jcf(4,3) = 0.0_wp/1.0_wp jcf(5,3) = 0.0_wp/1.0_wp jcf(1,4) = 0.0_wp/1.0_wp jcf(2,4) = 0.0_wp/1.0_wp jcf(3,4) = 1.0_wp/1.0_wp jcf(4,4) = 81.0_wp/500.0_wp jcf(5,4) = 0.0_wp/1.0_wp jcf(1,5) = 0.0_wp/1.0_wp jcf(2,5) = 0.0_wp/1.0_wp jcf(3,5) = 0.0_wp/1.0_wp jcf(4,5) = 1.0_wp/1.0_wp jcf(5,5) = 81.0_wp/500.0_wp q(1,1) = 58996444619195.0_wp/1818053669131507.0_wp q(1,2) = 257667362574373.0_wp/1213506489053108.0_wp q(1,3) = 391906679010757.0_wp/1101145230479827.0_wp q(1,4) = -129959203618871.0_wp/247234713373779.0_wp q(1,5) = -129726922309611.0_wp/174783669444784.0_wp q(2,1) = 17986809694499.0_wp/221662627737099.0_wp q(2,2) = -1209910883141.0_wp/1272087693795296.0_wp q(2,3) = 821449782300429.0_wp/1140098821610971.0_wp q(2,4) = -1170342154359093.0_wp/3370142486610709.0_wp q(2,5) = 145361029450285.0_wp/244420429773343.0_wp q(3,1) = -96108943234752.0_wp/877526244101327.0_wp q(3,2) = -722317584455991.0_wp/933305545723805.0_wp q(3,3) = -215359600448925.0_wp/762621487786253.0_wp q(3,4) = -404029055113205.0_wp/727674537057372.0_wp q(3,5) = 26977838814835.0_wp/853262473235316.0_wp q(4,1) = 160773161249767.0_wp/327772117426808.0_wp q(4,2) = -886814598098661.0_wp/1589823652237292.0_wp q(4,3) = 587118028422419.0_wp/1483086341212028.0_wp q(4,4) = 513070839261098.0_wp/1106546348572213.0_wp q(4,5) = -142780424518803.0_wp/516047902827005.0_wp q(5,1) = 1024049504035917.0_wp/1190615019085042.0_wp q(5,2) = 101228853452082.0_wp/478313077676327.0_wp q(5,3) = -332553195684478.0_wp/969191661826049.0_wp q(5,4) = -93800103224574.0_wp/332000019662357.0_wp q(5,5) = 184964671986740.0_wp/1383350542885147.0_wp ! ======= t(1,1) = 81.0_wp/500.0_wp t(1,2) = -821468972980167.0_wp/2224965834444953.0_wp t(1,3) = 221118084821687.0_wp/560477703542195.0_wp t(1,4) = 10863362173142.0_wp/1071271522134629.0_wp t(1,5) = -1653126362612113.0_wp/1159492216630822.0_wp t(2,1) = 0.0_wp/1.0_wp t(2,2) = 81.0_wp/500.0_wp t(2,3) = -215454124843346.0_wp/913832121515455.0_wp t(2,4) = 54785093288519.0_wp/454210658532458.0_wp t(2,5) = 1769398064220510.0_wp/2073579293259967.0_wp t(3,1) = 0.0_wp/1.0_wp t(3,2) = 0.0_wp/1.0_wp t(3,3) = 81.0_wp/500.0_wp t(3,4) = 315456619398913.0_wp/1705679753787811.0_wp t(3,5) = -1275686337862817.0_wp/1219503721825754.0_wp t(4,1) = 0.0_wp/1.0_wp t(4,2) = 0.0_wp/1.0_wp t(4,3) = 0.0_wp/1.0_wp t(4,4) = 81.0_wp/500.0_wp t(4,5) = 1561715024994547.0_wp/1266799612689913.0_wp t(5,1) = 0.0_wp/1.0_wp t(5,2) = 0.0_wp/1.0_wp t(5,3) = 0.0_wp/1.0_wp t(5,4) = 0.0_wp/1.0_wp t(5,5) = 81.0_wp/500.0_wp !===================================================================================================================120 !===================================================================================================================120 ! ********************* SIRK4(3)5L[3]SA ********************* !===================================================================================================================120 !===================================================================================================================120 ! SIRK, 5-stage, order =4, stage-order = 3, ! Stiffly-accurate, internally L-stable on ALL stages ! ! D = 1.5972 ! Min{a,b} = {-1.5972, -1.06132} ! Max{a,b} = {1.56981, 1.32712} ! {Min.,Max} Eig(M), = {-0.143859, 5.13} ! Cmeasure = 0.34291 ! {Min., Max., RMS} Eig(M)int = {-0.253941, -0.125736, 0.367617} ! Condition Number of S, kappaI(S)_{2,Inf} = {1248.23, 2246.51} ! ! 17 55 62 41 ! c = {--, ---, --, --, 1}, {cmin,cmax} = {0.346939, 0.891304} ! 49 107 71 46 ! ! g = 31/125 (= 0.248) ! ! {A1,A2,A3,A4,A5,A6,A7} = {0, 0, 0, 0, 0.0071442977, 0.018571746, 0.030284345} ! Embedded method ! {A1,A2,A3,A4,A5,A6,A7} = {0, 0, 0, 0.023798698, 0.058261111, 0.094971090, 0.12609036} ! B,C,E = {2.44808, 2.15174, 0.300197} !============================================================== !===================================================================================================================120 casename='SIRK4[3]5L[3]SA' ! SIRK4(3)5L[3]SA !===================================================================================================================120 ns = 5 aI(1,1) = 2561764438911047.0_wp/1939789253777994.0_wp aI(2,1) = 583764573708861.0_wp/381129116922874.0_wp aI(3,1) = 697014030698718.0_wp/502721655507907.0_wp aI(4,1) = 31197241638190267.0_wp/19873208737963304.0_wp aI(5,1) = 513361653177515.0_wp/386823049866276.0_wp aI(1,2) = -1632682096348781.0_wp/1145312109265568.0_wp aI(2,2) = -835098527363259.0_wp/522851745095743.0_wp aI(3,2) = -1772772827174231.0_wp/1502834578192291.0_wp aI(4,2) = -647383974885653.0_wp/422479248163463.0_wp aI(5,2) = -691676781603508.0_wp/651711025093649.0_wp aI(1,3) = 235429318632550.0_wp/446580178534171.0_wp aI(2,3) = 645805423011557.0_wp/778711094908326.0_wp aI(3,3) = 904466620498489.0_wp/806555106243156.0_wp aI(4,3) = 578642772887107.0_wp/635344161767978.0_wp aI(5,3) = 782479806459993.0_wp/1003344489740524.0_wp aI(1,4) = 753193691149766.0_wp/1629115422698627.0_wp aI(2,4) = 3858731724206175.0_wp/7955887253791259.0_wp aI(3,4) = 12714387171186.0_wp/78374591819131.0_wp aI(4,4) = 692734315342246.0_wp/767155189738535.0_wp aI(5,4) = 553664976816304.0_wp/1198001794678177.0_wp aI(1,5) = -932937740852569.0_wp/1735108233142127.0_wp aI(2,5) = -941823920383309.0_wp/1281750181102200.0_wp aI(3,5) = -531194532852658.0_wp/860592577411115.0_wp aI(4,5) = -1501956758189227.0_wp/1564684009360966.0_wp aI(5,5) = -207922402463867.0_wp/409435549695520.0_wp ! ======= bE(1) = 513361653177515.0_wp/386823049866276.0_wp bE(2) = -691676781603508.0_wp/651711025093649.0_wp bE(3) = 782479806459993.0_wp/1003344489740524.0_wp bE(4) = 553664976816304.0_wp/1198001794678177.0_wp bE(5) = -207922402463867.0_wp/409435549695520.0_wp ! ======= bEh(1) = 2135761529758181.0_wp/1061388085349794.0_wp bEh(2) = -1335550384883183.0_wp/560757396067403.0_wp bEh(3) = 189667883158228.0_wp/1357459306710033.0_wp bEh(4) = 916505133693061.0_wp/305927250903775.0_wp bEh(5) = -536210124226979.0_wp/303613600464194.0_wp ! ======= cE(1) = 17.0_wp/49.0_wp cE(2) = 55.0_wp/107.0_wp cE(3) = 62.0_wp/71.0_wp cE(4) = 41.0_wp/46.0_wp cE(5) = 1.0_wp/1.0_wp ! ======= g = 31.0_wp/125.0_wp ! ======= s(1,1) = -739540252028217.0_wp/1062133454324600.0_wp s(2,1) = 13751344334966.0_wp/910866302167435.0_wp s(3,1) = 1704947208291831.0_wp/870789888689183.0_wp s(4,1) = 2723342706436538.0_wp/2366889332763985.0_wp s(5,1) = 37.0_wp/25.0_wp s(1,2) = -1553566520184106.0_wp/473998207975133.0_wp s(2,2) = 188518317606091.0_wp/105941493147130.0_wp s(3,2) = 9457792056762790.0_wp/872675955048243.0_wp s(4,2) = 1133291745363965.0_wp/919892611548549.0_wp s(5,2) = 431.0_wp/250.0_wp s(1,3) = -25409409448482083.0_wp/721731674723392.0_wp s(2,3) = -11793427445119267.0_wp/2048611382806928.0_wp s(3,3) = 47278440143080229.0_wp/750308866304997.0_wp s(4,3) = -16583298057351821.0_wp/1055232019553414.0_wp s(5,3) = -607.0_wp/1000.0_wp s(1,4) = -167194631332295821.0_wp/1262633007220385.0_wp s(2,4) = -12858180168276271.0_wp/929524326053477.0_wp s(3,4) = 351477840508949081.0_wp/1211494102280202.0_wp s(4,4) = -66749741583564457.0_wp/468751209344093.0_wp s(5,4) = -1.0_wp/1000.0_wp s(1,5) = 4958557695920099919.0_wp/7561081995727460.0_wp s(2,5) = 79512605492257990.0_wp/574280345994617.0_wp s(3,5) = -129782926327350431.0_wp/385477027326353.0_wp s(4,5) = -626809857484413233.0_wp/628636928086386.0_wp s(5,5) = -1.0_wp/1000.0_wp ! ======= sinv(1,1) = -19030894506373.0_wp/783898335716680.0_wp sinv(2,1) = 159833418209084.0_wp/750485919144727.0_wp sinv(3,1) = 200638446958329.0_wp/367556234502709.0_wp sinv(4,1) = -94875361038769.0_wp/812854647019161.0_wp sinv(5,1) = 6502097381837.0_wp/783321790492115.0_wp sinv(1,2) = -549929129480103.0_wp/1315721146711016.0_wp sinv(2,2) = 165783505389017.0_wp/1359862769003125.0_wp sinv(3,2) = -1458510345194611.0_wp/2167015606097852.0_wp sinv(4,2) = 122459931453855.0_wp/912911365738826.0_wp sinv(5,2) = -3817234591063.0_wp/429817241344129.0_wp sinv(1,3) = -60988890005168.0_wp/1055917602322697.0_wp sinv(2,3) = 132947804211473.0_wp/860626084359894.0_wp sinv(3,3) = 510325369512937.0_wp/1712424974934677.0_wp sinv(4,3) = -59692428714701.0_wp/966906177256150.0_wp sinv(5,3) = 7493134911839.0_wp/1765625789189927.0_wp sinv(1,4) = -36356426660968.0_wp/667041659234597.0_wp sinv(2,4) = 204577468549465.0_wp/1951286755367513.0_wp sinv(3,4) = 139628742519680.0_wp/846549197090701.0_wp sinv(4,4) = -42603831987963.0_wp/1142359247229962.0_wp sinv(5,4) = 3237486206379.0_wp/1808339553741950.0_wp sinv(1,5) = 496799403360900.0_wp/631014979563743.0_wp sinv(2,5) = -120378188384469.0_wp/644010775267813.0_wp sinv(3,5) = -259011943510454.0_wp/1000806430726481.0_wp sinv(4,5) = 34600547475634.0_wp/636203754154603.0_wp sinv(5,5) = -516766192859.0_wp/171654701929353.0_wp ! ======= jcf(1,1) = 31.0_wp/125.0_wp jcf(2,1) = 0.0_wp/1.0_wp jcf(3,1) = 0.0_wp/1.0_wp jcf(4,1) = 0.0_wp/1.0_wp jcf(5,1) = 0.0_wp/1.0_wp jcf(1,2) = 1.0_wp/1.0_wp jcf(2,2) = 31.0_wp/125.0_wp jcf(3,2) = 0.0_wp/1.0_wp jcf(4,2) = 0.0_wp/1.0_wp jcf(5,2) = 0.0_wp/1.0_wp jcf(1,3) = 0.0_wp/1.0_wp jcf(2,3) = 1.0_wp/1.0_wp jcf(3,3) = 31.0_wp/125.0_wp jcf(4,3) = 0.0_wp/1.0_wp jcf(5,3) = 0.0_wp/1.0_wp jcf(1,4) = 0.0_wp/1.0_wp jcf(2,4) = 0.0_wp/1.0_wp jcf(3,4) = 1.0_wp/1.0_wp jcf(4,4) = 31.0_wp/125.0_wp jcf(5,4) = 0.0_wp/1.0_wp jcf(1,5) = 0.0_wp/1.0_wp jcf(2,5) = 0.0_wp/1.0_wp jcf(3,5) = 0.0_wp/1.0_wp jcf(4,5) = 1.0_wp/1.0_wp jcf(5,5) = 31.0_wp/125.0_wp ! ======= q(1,1) = 289524601441849.0_wp/1163754812599436.0_wp q(1,2) = -546821194740631.0_wp/4115188022723108.0_wp q(1,3) = 557532964956161.0_wp/947600216511289.0_wp q(1,4) = 373164661075327.0_wp/862225623560992.0_wp q(1,5) = 274956941376109.0_wp/442004411938755.0_wp q(2,1) = -2897034983911.0_wp/537058957530267.0_wp q(2,2) = 166276355970087.0_wp/603947313506824.0_wp q(2,3) = 826067144943691.0_wp/1207278160319848.0_wp q(2,4) = 126172704185050.0_wp/1106049290674793.0_wp q(2,5) = -693404599172407.0_wp/1041830044755591.0_wp q(3,1) = -371662360502437.0_wp/531263242495828.0_wp q(3,2) = 843906991674039.0_wp/1334921484168332.0_wp q(3,3) = 29272408607167.0_wp/861040915283391.0_wp q(3,4) = 68345747963574.0_wp/735810691041119.0_wp q(3,5) = 276282699480821.0_wp/868688316169016.0_wp q(4,1) = -1068512218225985.0_wp/2599045573160872.0_wp q(4,2) = -642318160325479.0_wp/1434804383669820.0_wp q(4,3) = 395217551228836.0_wp/946086781884035.0_wp q(4,4) = -713006032435108.0_wp/1077265606922719.0_wp q(4,5) = 125775600196465.0_wp/937440325355191.0_wp q(5,1) = -354826832681789.0_wp/670986041300006.0_wp q(5,2) = -553669413225971.0_wp/1000100396693679.0_wp q(5,3) = -54978426456385.0_wp/550233142143992.0_wp q(5,4) = 572256519914321.0_wp/963194541676965.0_wp q(5,5) = -203709275719987.0_wp/902916506461602.0_wp ! ======= t(1,1) = 31.0_wp/125.0_wp t(1,2) = -218161015330634.0_wp/488813283049989.0_wp t(1,3) = -310236932935181.0_wp/713056372909934.0_wp t(1,4) = 79053222139850.0_wp/454921202677941.0_wp t(1,5) = -2065476230425378.0_wp/663304906588651.0_wp t(2,1) = 0.0_wp/1.0_wp t(2,2) = 31.0_wp/125.0_wp t(2,3) = -183627552950816.0_wp/849644506746337.0_wp t(2,4) = 313461285599657.0_wp/943957943401370.0_wp t(2,5) = -2899873397162253.0_wp/6045987949750568.0_wp t(3,1) = 0.0_wp/1.0_wp t(3,2) = 0.0_wp/1.0_wp t(3,3) = 31.0_wp/125.0_wp t(3,4) = -4385105261628083.0_wp/9416881624874393.0_wp t(3,5) = 1133581789376847.0_wp/287708408915756.0_wp t(4,1) = 0.0_wp/1.0_wp t(4,2) = 0.0_wp/1.0_wp t(4,3) = 0.0_wp/1.0_wp t(4,4) = 31.0_wp/125.0_wp t(4,5) = 4782502237767455.0_wp/5752132869594289.0_wp t(5,1) = 0.0_wp/1.0_wp t(5,2) = 0.0_wp/1.0_wp t(5,3) = 0.0_wp/1.0_wp t(5,4) = 0.0_wp/1.0_wp t(5,5) = 31.0_wp/125.0_wp !===================================================================================================================120 casename='SIRK4[3]5L[3]DAE' ! SIRK4[3]5L3DAE !===================================================================================================================120 ns=5 aI(1,1) = 2163379198141835.0_wp/1640826866323033.0_wp aI(2,1) = 443097036596831.0_wp/332992471326931.0_wp aI(3,1) = 509639708599403.0_wp/342554445112672.0_wp aI(4,1) = 1222583151962167.0_wp/904519827600234.0_wp aI(5,1) = 1145761197516913.0_wp/863390004168396.0_wp aI(1,2) = -570409200931280.0_wp/1190435699078571.0_wp aI(2,2) = 227033802713141.0_wp/708813421390000.0_wp aI(3,2) = -394444743246067.0_wp/1594625692991241.0_wp aI(4,2) = 74285729289221.0_wp/924475593480948.0_wp aI(5,2) = -328230397417730.0_wp/762988654391927.0_wp aI(1,3) = -729531443400332.0_wp/758852487599661.0_wp aI(2,3) = -580659553554776.0_wp/347454385662463.0_wp aI(3,3) = -632358346407853.0_wp/482359759787489.0_wp aI(4,3) = -1304228520436523.0_wp/1023979791612780.0_wp aI(5,3) = -73538703567283.0_wp/115741063800379.0_wp aI(1,4) = 789322370911752.0_wp/801386511500251.0_wp aI(2,4) = 279901781570185.0_wp/258875066709099.0_wp aI(3,4) = 1367984898267443.0_wp/1050895762749004.0_wp aI(4,4) = 1921815345767198.0_wp/1383233294574233.0_wp aI(5,4) = 630780663168029.0_wp/518870627875254.0_wp aI(1,5) = -222110870523003.0_wp/429831326392282.0_wp aI(2,5) = -403099051436876.0_wp/712608105163607.0_wp aI(3,5) = -529737618101915.0_wp/750426648151257.0_wp aI(4,5) = -491443400351000.0_wp/731389306759893.0_wp aI(5,5) = -537147240872996.0_wp/1125702104042575.0_wp ! ======= bE(1) = 1145761197516913.0_wp/863390004168396.0_wp bE(2) = -328230397417730.0_wp/762988654391927.0_wp bE(3) = -73538703567283.0_wp/115741063800379.0_wp bE(4) = 630780663168029.0_wp/518870627875254.0_wp bE(5) = -537147240872996.0_wp/1125702104042575.0_wp ! ======= bEh(1) = 701934182912138.0_wp/402420699416543.0_wp bEh(2) = -817175541417889.0_wp/370065423339290.0_wp bEh(3) = 721163457097716.0_wp/1316429992865273.0_wp bEh(4) = 3226675500258391.0_wp/1874908829397206.0_wp bEh(5) = -1700169387246032.0_wp/2112320615424847.0_wp ! ======= cE(1) = 9.0_wp/26.0_wp cE(2) = 53.0_wp/107.0_wp cE(3) = 52.0_wp/99.0_wp cE(4) = 148.0_wp/169.0_wp cE(5) = 1.0_wp/1.0_wp ! ======= g = 31.0_wp/125.0_wp ! !===================================================================================================================120 !===================================================================================================================120 ! ********************* SIRK5(4)5L[3]SA ********************* !===================================================================================================================120 !===================================================================================================================120 ! SIRK, 5-stage, order = 5, stage-order = 3, ! Stiffly-accurate, internally L-stable on ALL stages ! ! D = 7.84944 ! Min{a,b} = {-7.8494, -7.1512} ! Max{a,b} = {5.7127, 5.1718} ! {Min.,Max} Eig(M), = {-0.562141, 39.3688} ! Cmeasure = 0.244489 ! {Min., Max., RMS} Eig(M)int = {-2.10991, -0.985011, 2.87429} !ondition Number of S, kappa(S)_{2,Inf} = {3016.23, 4942.08} ! ! 500 438 1826 586 ! c = {----, ---, ----, ---, 1}, {cmin,cmax} = {0.389712, 0.900154} ! 1283 929 2635 651 ! ! g = 462534531056787/1663471107488864 =~ 0.278054 ! ! {A1,A2,A3,A4,A5,A6,A7} = {0, 0, 0, 0, 0.0055257194, 0.014033599, 0.020816808} ! Embedded method ! {A1,A2,A3,A4,A5,A6,A7} = {0, 0, 0, 0, 0, 0.0028728564, 0.010577203, 0.023201007} ! B,C,E = {3.6818, 2.84087, 1.24819} !============================================================== !===================================================================================================================120 casename='SIRK5[4]5L[3]SA' ! SIRK5(4)5L[3]SA !===================================================================================================================120 ns = 5 aI(1,1) = 2957049942028058.0_wp/876045806633349.0_wp aI(2,1) = 5782601018059159.0_wp/1420606742941844.0_wp aI(3,1) = 7394083672781104.0_wp/1319945803780631.0_wp aI(4,1) = 1708518008575793.0_wp/299075407615103.0_wp aI(5,1) = 22282049043593853.0_wp/4308368588372464.0_wp aI(1,2) = -7367890837823199.0_wp/1876855807279201.0_wp aI(2,2) = -3780135671512331.0_wp/757609492392709.0_wp aI(3,2) = -8950380810148821.0_wp/1187320031645512.0_wp aI(4,2) = -5400512213871233.0_wp/688012371705711.0_wp aI(5,2) = -9770202945607981.0_wp/1366223293570423.0_wp aI(1,3) = 1199044101003599.0_wp/1188831840677425.0_wp aI(2,3) = 2937161236252365.0_wp/1689468692888797.0_wp aI(3,3) = 3375736202914051.0_wp/889671208768069.0_wp aI(4,3) = 2641426696311999.0_wp/594917923091426.0_wp aI(5,3) = 4032747790297437.0_wp/876818153986988.0_wp aI(1,4) = 1248115473413211.0_wp/6584668783623740.0_wp aI(2,4) = -205751551717192.0_wp/1001641746157963.0_wp aI(3,4) = -3002156479453317.0_wp/2044522098300845.0_wp aI(4,4) = -1125611165168923.0_wp/545842097353498.0_wp aI(5,4) = -3904193967064637.0_wp/1349987776494300.0_wp aI(1,5) = -399029564166168.0_wp/1545295130760569.0_wp aI(2,5) = -104674590900190.0_wp/734142050582233.0_wp aI(3,5) = 91322401030988.0_wp/300895169052357.0_wp aI(4,5) = 562046211519962.0_wp/852750518279525.0_wp aI(5,5) = 17145800759.0_wp/13477640670.0_wp !================================================================ bE(1) = 22282049043593853.0_wp/4308368588372464.0_wp bE(2) = -9770202945607981.0_wp/1366223293570423.0_wp bE(3) = 4032747790297437.0_wp/876818153986988.0_wp bE(4) = -3904193967064637.0_wp/1349987776494300.0_wp bE(5) = 17145800759.0_wp/13477640670.0_wp !================================================================ bEh(1) = 6683572101201647.0_wp/1140236019835067.0_wp bEh(2) = -6965102855558180.0_wp/824301485227613.0_wp bEh(3) = 5142000300260830.0_wp/879537376700627.0_wp bEh(4) = -4453112745386595.0_wp/1094364347301302.0_wp bEh(5) = 152550917183879.0_wp/84235254187500.0_wp !================================================================ cE(1) = 500.0_wp/1283.0_wp cE(2) = 438.0_wp/929.0_wp cE(3) = 1826.0_wp/2635.0_wp cE(4) = 586.0_wp/651.0_wp cE(5) = 1.0_wp/1.0_wp g = 462534531056787.0_wp/1663471107488864.0_wp ! ======= s(1,1) = -269391931013638.0_wp/850158827817133.0_wp s(2,1) = -430838761533856.0_wp/2033108065317145.0_wp s(3,1) = 121381775551961.0_wp/453367766743693.0_wp s(4,1) = 738455072263007.0_wp/1015936793176499.0_wp s(5,1) = 1.0_wp/1.0_wp s(1,2) = 212218349895287.0_wp/635323701503552.0_wp s(2,2) = 894977733977374.0_wp/1777527454117581.0_wp s(3,2) = 681106732829453.0_wp/1097027761811874.0_wp s(4,2) = -3100614662707.0_wp/511504308025453.0_wp s(5,2) = 0.0_wp/1.0_wp s(1,3) = -5672702329144883.0_wp/1075341377633883.0_wp s(2,3) = -13589705861535386.0_wp/2276367691576887.0_wp s(3,3) = -3379599901252481.0_wp/569646665326610.0_wp s(4,3) = -1547214171598737.0_wp/376742206873558.0_wp s(5,3) = 0.0_wp/1.0_wp s(1,4) = 19543072124191941.0_wp/1312611577963498.0_wp s(2,4) = 11444010408420148.0_wp/969445179072283.0_wp s(3,4) = -5216142654719923.0_wp/1497179385956031.0_wp s(4,4) = -10702605946281433.0_wp/1320441630140714.0_wp s(5,4) = 0.0_wp/1.0_wp s(1,5) = 155520650954127495.0_wp/717715530007346.0_wp s(2,5) = 203048623651878290.0_wp/1154561448226393.0_wp s(3,5) = 61803653847849379.0_wp/1879036720131629.0_wp s(4,5) = 2455880245482626.0_wp/497301300039821.0_wp s(5,5) = 0.0_wp/1.0_wp ! ======= sinv(1,1) = 0.0_wp/1.0_wp sinv(2,1) = 22282049043593853.0_wp/4308368588372464.0_wp sinv(3,1) = 1124446590516028.0_wp/868659083274985.0_wp sinv(4,1) = -391255061667943.0_wp/634357385007932.0_wp sinv(5,1) = 59617380855292.0_wp/845221780706827.0_wp sinv(1,2) = 0.0_wp/1.0_wp sinv(2,2) = -9770202945607981.0_wp/1366223293570423.0_wp sinv(3,2) = -1276607913707113.0_wp/745663411500127.0_wp sinv(4,2) = 576554466277027.0_wp/703276377431405.0_wp sinv(5,2) = -46043418961309.0_wp/529325656313247.0_wp sinv(1,3) = 0.0_wp/1.0_wp sinv(2,3) = 4032747790297437.0_wp/876818153986988.0_wp sinv(3,3) = 122043592680941.0_wp/177403071342020.0_wp sinv(4,3) = -213594901712761.0_wp/642937621882394.0_wp sinv(5,3) = 24926960314129.0_wp/767344989149062.0_wp sinv(1,4) = 0.0_wp/1.0_wp sinv(2,4) = -3904193967064637.0_wp/1349987776494300.0_wp sinv(3,4) = -286610670955141.0_wp/696763782190993.0_wp sinv(4,4) = 42434471729240.0_wp/527428757364281.0_wp sinv(5,4) = -8828723041864.0_wp/796519698884445.0_wp sinv(1,5) = 1.0_wp/1.0_wp sinv(2,5) = 1803891326302103.0_wp/1814574642494473.0_wp sinv(3,5) = 303142415479667.0_wp/1869089348373532.0_wp sinv(4,5) = 4890748252162.0_wp/558695846343827.0_wp sinv(5,5) = 3633374902683.0_wp/1108805067227771.0_wp jcf(1,1) = 462534531056787.0_wp/1663471107488864.0_wp jcf(2,1) = 0.0_wp/1.0_wp jcf(3,1) = 0.0_wp/1.0_wp jcf(4,1) = 0.0_wp/1.0_wp jcf(5,1) = 0.0_wp/1.0_wp jcf(1,2) = 1.0_wp/1.0_wp jcf(2,2) = 462534531056787.0_wp/1663471107488864.0_wp jcf(3,2) = 0.0_wp/1.0_wp jcf(4,2) = 0.0_wp/1.0_wp jcf(5,2) = 0.0_wp/1.0_wp jcf(1,3) = 0.0_wp/1.0_wp jcf(2,3) = 1.0_wp/1.0_wp jcf(3,3) = 462534531056787.0_wp/1663471107488864.0_wp jcf(4,3) = 0.0_wp/1.0_wp jcf(5,3) = 0.0_wp/1.0_wp jcf(1,4) = 0.0_wp/1.0_wp jcf(2,4) = 0.0_wp/1.0_wp jcf(3,4) = 1.0_wp/1.0_wp jcf(4,4) = 462534531056787.0_wp/1663471107488864.0_wp jcf(5,4) = 0.0_wp/1.0_wp jcf(1,5) = 0.0_wp/1.0_wp jcf(2,5) = 0.0_wp/1.0_wp jcf(3,5) = 0.0_wp/1.0_wp jcf(4,5) = 1.0_wp/1.0_wp jcf(5,5) = 462534531056787.0_wp/1663471107488864.0_wp ! ======= q(1,1) = -158421375028944.0_wp/660494135853625.0_wp q(1,2) = -135662191692539.0_wp/361483225546080.0_wp q(1,3) = 191740524886703.0_wp/430237920399382.0_wp q(1,4) = 256677060523021.0_wp/523213641501330.0_wp q(1,5) = 350847946071506.0_wp/582851597367183.0_wp q(2,1) = -124819389415603.0_wp/778157397500910.0_wp q(2,2) = -2604034378518969.0_wp/4531811458828265.0_wp q(2,3) = 69235042660345.0_wp/543266928285804.0_wp q(2,4) = 213481722920267.0_wp/770436179724267.0_wp q(2,5) = -526152259290423.0_wp/708774500504581.0_wp q(3,1) = 217653958337663.0_wp/1073997884058408.0_wp q(3,2) = -2059476955089430.0_wp/2835482370303217.0_wp q(3,3) = -190562380699463.0_wp/567725872950681.0_wp q(3,4) = -163443058066217.0_wp/332340199020697.0_wp q(3,5) = 269967866159701.0_wp/973811004977446.0_wp q(4,1) = 1048493143056392.0_wp/1905670925005897.0_wp q(4,2) = -15579948010040.0_wp/895282992111053.0_wp q(4,3) = 813569626792337.0_wp/1064575519239127.0_wp q(4,4) = -696911782823636.0_wp/2161016421739333.0_wp q(4,5) = -26977595856449.0_wp/285195807667627.0_wp q(5,1) = 723096924940391.0_wp/955292167314234.0_wp q(5,2) = -38116519686868.0_wp/1135210118426779.0_wp q(5,3) = -379336635479412.0_wp/1275519796535263.0_wp q(5,4) = 1738528953824046.0_wp/2996172173963285.0_wp q(5,5) = 10257972467219.0_wp/366815589029066.0_wp ! ======= t(1,1) = 462534531056787.0_wp/1663471107488864.0_wp t(1,2) = -1367995668196441.0_wp/896233813350642.0_wp t(1,3) = -8277242252878787.0_wp/2364952501061068.0_wp t(1,4) = -342630589823929.0_wp/993073805297501.0_wp t(1,5) = 18295767145179029.0_wp/1384701755305125.0_wp t(2,1) = 0.0_wp/1.0_wp t(2,2) = 462534531056787.0_wp/1663471107488864.0_wp t(2,3) = 163248020801414.0_wp/803286658425581.0_wp t(2,4) = 334091934707342.0_wp/543667918766043.0_wp t(2,5) = -13485733648205469.0_wp/985734587366036.0_wp t(3,1) = 0.0_wp/1.0_wp t(3,2) = 0.0_wp/1.0_wp t(3,3) = 462534531056787.0_wp/1663471107488864.0_wp t(3,4) = -310400074820811.0_wp/1086120415763042.0_wp t(3,5) = 3634376055852039.0_wp/732486316263583.0_wp t(4,1) = 0.0_wp/1.0_wp t(4,2) = 0.0_wp/1.0_wp t(4,3) = 0.0_wp/1.0_wp t(4,4) = 462534531056787.0_wp/1663471107488864.0_wp t(4,5) = 7510414847390378.0_wp/4300981426270077.0_wp t(5,1) = 0.0_wp/1.0_wp t(5,2) = 0.0_wp/1.0_wp t(5,3) = 0.0_wp/1.0_wp t(5,4) = 0.0_wp/1.0_wp t(5,5) = 462534531056787.0_wp/1663471107488864.0_wp !===================================================================================================================120 !===================================================================================================================120 ! ********************* SIRK4(3)6L[4]SA ********************* !===================================================================================================================120 !===================================================================================================================120 ! ! SIRK, 6-stage, order =4, stage-order = 4, ! Stiffly-accurate, internally L-stable on ALL stages ! ! D = 1.04976 ! Min{a,b} = {-1.04976, -0.982557} ! Max{a,b} = {1.04415, 1.04415} ! {Min.,Max} Eig(M), = {-0.243363, 2.24862} ! Cmeasure = 0.392851 ! {Min., Max., RMS} Eig(M)int = {-0.297572, -0.159425, 0.521889} ! Condition Number of S, kappaI(S)_{2,Inf} = {2499.62, 4152.18} ! ! 24 20 17 6 35 ! c = {---, --, --, -, --, 1}, ! 109 33 52 7 48 ! ! g = 19/100 ! ! {A1,A2,A3,A4,A5,A6,A7} = {0, 0, 0, 0, 0.0018973666, 0.0055294582, 0.0099492401} ! Embedded method ! {A1,A2,A3,A4,A5,A6,A7} = {0, 0, 0, 0.0020992456, 0.0037943537, 0.0037140731, 0.0032386718} ! B,C,E = {1.80748, 2.71132, 0.903833} !============================================================== !===================================================================================================================120 casename='SIRK4[3]6L[4]SA' ! SIRK4(3)6L[4]SA !===================================================================================================================120 ns = 6 aI(1,1) = 2336787847068001.0_wp/2577597209547077.0_wp aI(2,1) = 1303373347362601.0_wp/1421071765691043.0_wp aI(3,1) = 1550390398362573.0_wp/1558870192991855.0_wp aI(4,1) = 441921432010484.0_wp/490393908566383.0_wp aI(5,1) = 1266214116743344.0_wp/1253783462082657.0_wp aI(6,1) = 1385663128040700.0_wp/1327077573237439.0_wp aI(1,2) = 184181518573427.0_wp/367545806244361.0_wp aI(2,2) = 638122698474866.0_wp/891131705234247.0_wp aI(3,2) = 805813171551199.0_wp/1203788602791491.0_wp aI(4,2) = 254027129987149.0_wp/512176380576381.0_wp aI(5,2) = 664889167992880.0_wp/1141998771500451.0_wp aI(6,2) = 1003869408750454.0_wp/1435056349422203.0_wp aI(1,3) = -1176370393322581.0_wp/1183614399998885.0_wp aI(2,3) = -1814595755870581.0_wp/2373646754872588.0_wp aI(3,3) = -608814087551129.0_wp/597908835631392.0_wp aI(4,3) = -427524720938786.0_wp/598658636359573.0_wp aI(5,3) = -1225448219131643.0_wp/1342971467831446.0_wp aI(6,3) = -1284915601194427.0_wp/1307725860796871.0_wp aI(1,4) = -388820208129589.0_wp/995235974449893.0_wp aI(2,4) = -103071312929787.0_wp/278696656719829.0_wp aI(3,4) = -302205448115847.0_wp/908106608262061.0_wp aI(4,4) = -191226066685539.0_wp/308818705345568.0_wp aI(5,4) = -672738007412623.0_wp/640850097512132.0_wp aI(6,4) = -3952719904197168.0_wp/4639929430019699.0_wp aI(1,5) = 68918101404262.0_wp/1142193133663625.0_wp aI(2,5) = -21448090630146.0_wp/771271351384927.0_wp aI(3,5) = -77979084958639.0_wp/641948067716429.0_wp aI(4,5) = 746979177137745.0_wp/1258092448220744.0_wp aI(5,5) = 342183731841472.0_wp/440133265132407.0_wp aI(6,5) = 2126364384743569.0_wp/2980500007713724.0_wp aI(1,6) = 79942680880535.0_wp/584724670267658.0_wp aI(2,6) = 162583302861941.0_wp/1205025499674641.0_wp aI(3,6) = 180815339552081.0_wp/1334794232419763.0_wp aI(4,6) = 114066996283037.0_wp/571400458575477.0_wp aI(5,6) = 217413543090059.0_wp/675552070935089.0_wp aI(6,6) = 316967309207526.0_wp/839993898697303.0_wp ! ======= bE(1) = 1385663128040700.0_wp/1327077573237439.0_wp bE(2) = 1003869408750454.0_wp/1435056349422203.0_wp bE(3) = -1284915601194427.0_wp/1307725860796871.0_wp bE(4) = -3952719904197168.0_wp/4639929430019699.0_wp bE(5) = 2126364384743569.0_wp/2980500007713724.0_wp bE(6) = 316967309207526.0_wp/839993898697303.0_wp ! ======= bEh(1) = 763634524559279.0_wp/865195452834827.0_wp bEh(2) = 1385893896792718.0_wp/2580895821446749.0_wp bEh(3) = -715438867383588.0_wp/1085711292766657.0_wp bEh(4) = 2546219819722.0_wp/1171257634643167.0_wp bEh(5) = 110197627399649.0_wp/687625425311110.0_wp bEh(6) = 62385229158339.0_wp/810937590128560.0_wp ! ======= cE(1) = 24.0_wp/109.0_wp cE(2) = 20.0_wp/33.0_wp cE(3) = 17.0_wp/52.0_wp cE(4) = 6.0_wp/7.0_wp cE(5) = 35.0_wp/48.0_wp cE(6) = 1.0_wp/1.0_wp ! ======= g = 19.0_wp/100.0_wp ! ======= ! CN of S, kappaI(S)_{2,Inf} = {2499.62, 4152.18} ! ======= s(1,1) = 361670948911398.0_wp/1056409507810919.0_wp s(2,1) = -66382956402216.0_wp/215759354446645.0_wp s(3,1) = -196277424613116.0_wp/2609315130025453.0_wp s(4,1) = 867047856891777.0_wp/549642732821000.0_wp s(5,1) = 17564350954566097.0_wp/21700275757056000.0_wp s(6,1) = 2937.0_wp/1000.0_wp s(1,2) = -735962336957851.0_wp/965766361059446.0_wp s(2,2) = 3753120490977303.0_wp/949697001302957.0_wp s(3,2) = -615139447604293.0_wp/1608216208622966.0_wp s(4,2) = 2778984376997577.0_wp/470762464379684.0_wp s(5,2) = 6549569528162289.0_wp/922499223732424.0_wp s(6,2) = 371.0_wp/125.0_wp s(1,3) = 52165808511448316.0_wp/3563317281160651.0_wp s(2,3) = -9017257556989925.0_wp/688242475643181.0_wp s(3,3) = 1592887907678929.0_wp/192789924382969.0_wp s(4,3) = -50550747381782407.0_wp/5187626156782511.0_wp s(5,3) = -4321420791968333.0_wp/924258378828403.0_wp s(6,3) = -1.0_wp/1000.0_wp s(1,4) = -2729351081564518813.0_wp/36853636981259074.0_wp s(2,4) = 31985209698105760.0_wp/1555986230249067.0_wp s(3,4) = -73434939734155183.0_wp/1309204320789153.0_wp s(4,4) = -700986480103975.0_wp/75554144939924.0_wp s(5,4) = 3311005817137079.0_wp/795962242314405.0_wp s(6,4) = -2026.0_wp/125.0_wp s(1,5) = -87874403798019452.0_wp/1054761419929193.0_wp s(2,5) = 880961529734556778.0_wp/1522670647860977.0_wp s(3,5) = 541100914570671380.0_wp/1469280441682657.0_wp s(4,5) = -70115601225020949.0_wp/368068531023790.0_wp s(5,5) = -271974916011041228.0_wp/1466351137051487.0_wp s(6,5) = -1093.0_wp/100.0_wp s(1,6) = -560173489702449349.0_wp/1124691827539166.0_wp s(2,6) = 2965616740846378527.0_wp/595136221727639.0_wp s(3,6) = 825836801751893813.0_wp/364245064029897.0_wp s(4,6) = -433294088271282649.0_wp/1479935576391261.0_wp s(5,6) = -1017474731537589657.0_wp/727104917509994.0_wp s(6,6) = -9.0_wp/20.0_wp ! ======= sinv(1,1) = -46574653637993.0_wp/871406196924464.0_wp sinv(2,1) = 114367156940687.0_wp/836873112897162.0_wp sinv(3,1) = 98341866754459.0_wp/556540709600312.0_wp sinv(4,1) = 14908423129964.0_wp/717800674828213.0_wp sinv(5,1) = -3247968655861.0_wp/400123915587515.0_wp sinv(6,1) = 1401841793827.0_wp/1158822765152641.0_wp sinv(1,2) = -38158952403443.0_wp/1939728618672795.0_wp sinv(2,2) = 38972868134724.0_wp/358663346416183.0_wp sinv(3,2) = 324513635407776.0_wp/3039293894209447.0_wp sinv(4,2) = 39793277309884.0_wp/2059098493824545.0_wp sinv(5,2) = -1286966413839.0_wp/287178470324113.0_wp sinv(6,2) = 666467057002.0_wp/798530413918771.0_wp sinv(1,3) = -120619935868675.0_wp/2150405293952052.0_wp sinv(2,3) = -101686310399891.0_wp/939621382234133.0_wp sinv(3,3) = -168382380106883.0_wp/940163454896119.0_wp sinv(4,3) = -45616679293379.0_wp/1264853207039148.0_wp sinv(5,3) = 15287177248231.0_wp/1681644761636185.0_wp sinv(6,3) = -1040386729705.0_wp/803244461595036.0_wp sinv(1,4) = -42071214756527.0_wp/1136721172635148.0_wp sinv(2,4) = -122848286844607.0_wp/997988797584071.0_wp sinv(3,4) = -417904949630174.0_wp/2582228948244903.0_wp sinv(4,4) = -30514026443761.0_wp/1024458148716988.0_wp sinv(5,4) = 493055197791.0_wp/597980521772050.0_wp sinv(6,4) = -233099805644.0_wp/769202260343607.0_wp sinv(1,5) = -258374732706745.0_wp/1923926132734572.0_wp sinv(2,5) = 144393572268907.0_wp/765146147148988.0_wp sinv(3,5) = 53966635819133.0_wp/884883603217721.0_wp sinv(4,5) = 6526454620961.0_wp/707782293941288.0_wp sinv(5,5) = 1208381744507.0_wp/812517345988092.0_wp sinv(6,5) = -207056193263.0_wp/993964091074966.0_wp sinv(1,6) = 321472989018033.0_wp/803470408495442.0_wp sinv(2,6) = 5476743514478.0_wp/806712166784757.0_wp sinv(3,6) = 82983301322429.0_wp/1478746892061891.0_wp sinv(4,6) = 6786812600103.0_wp/559207992076904.0_wp sinv(5,6) = -42287166827.0_wp/295452071204453.0_wp sinv(6,6) = 83615240251.0_wp/626709748918192.0_wp ! ======= jcf(1,1) = 19.0_wp/100.0_wp jcf(2,1) = 0.0_wp/1.0_wp jcf(3,1) = 0.0_wp/1.0_wp jcf(4,1) = 0.0_wp/1.0_wp jcf(5,1) = 0.0_wp/1.0_wp jcf(6,1) = 0.0_wp/1.0_wp jcf(1,2) = 1.0_wp/1.0_wp jcf(2,2) = 19.0_wp/100.0_wp jcf(3,2) = 0.0_wp/1.0_wp jcf(4,2) = 0.0_wp/1.0_wp jcf(5,2) = 0.0_wp/1.0_wp jcf(6,2) = 0.0_wp/1.0_wp jcf(1,3) = 0.0_wp/1.0_wp jcf(2,3) = 1.0_wp/1.0_wp jcf(3,3) = 19.0_wp/100.0_wp jcf(4,3) = 0.0_wp/1.0_wp jcf(5,3) = 0.0_wp/1.0_wp jcf(6,3) = 0.0_wp/1.0_wp jcf(1,4) = 0.0_wp/1.0_wp jcf(2,4) = 0.0_wp/1.0_wp jcf(3,4) = 1.0_wp/1.0_wp jcf(4,4) = 19.0_wp/100.0_wp jcf(5,4) = 0.0_wp/1.0_wp jcf(6,4) = 0.0_wp/1.0_wp jcf(1,5) = 0.0_wp/1.0_wp jcf(2,5) = 0.0_wp/1.0_wp jcf(3,5) = 0.0_wp/1.0_wp jcf(4,5) = 1.0_wp/1.0_wp jcf(5,5) = 19.0_wp/100.0_wp jcf(6,5) = 0.0_wp/1.0_wp jcf(1,6) = 0.0_wp/1.0_wp jcf(2,6) = 0.0_wp/1.0_wp jcf(3,6) = 0.0_wp/1.0_wp jcf(4,6) = 0.0_wp/1.0_wp jcf(5,6) = 1.0_wp/1.0_wp jcf(6,6) = 19.0_wp/100.0_wp ! ======= q(1,1) = -57966413132662.0_wp/586207749955279.0_wp q(1,2) = 352057708646224.0_wp/2086510963393257.0_wp q(1,3) = -571857584421476.0_wp/799854626179871.0_wp q(1,4) = 283076480295193.0_wp/1129566760298442.0_wp q(1,5) = 153089439156025.0_wp/1054323995810236.0_wp q(1,6) = -902204898588125.0_wp/1489856570070767.0_wp q(2,1) = 157987417458904.0_wp/1777837228629795.0_wp q(2,2) = -484524752509064.0_wp/888286933878045.0_wp q(2,3) = 160035248186266.0_wp/621394761850497.0_wp q(2,4) = 208514649197963.0_wp/486538576211518.0_wp q(2,5) = -289531442198925.0_wp/557178943340651.0_wp q(2,6) = -464061628275629.0_wp/1110733061483550.0_wp q(3,1) = 22188420841393.0_wp/1021266363906106.0_wp q(3,2) = 26143816147109.0_wp/894781846277366.0_wp q(3,3) = -2001533569676298.0_wp/4414915204850063.0_wp q(3,4) = 399276353166871.0_wp/830969158606508.0_wp q(3,5) = -657296499982162.0_wp/1745039554018299.0_wp q(3,6) = 93240759126112.0_wp/143806991707523.0_wp q(4,1) = -404083653462232.0_wp/886880601092043.0_wp q(4,2) = -137507253328409.0_wp/384747330782248.0_wp q(4,3) = 96198597157231.0_wp/671528750165870.0_wp q(4,4) = 770873377029683.0_wp/1642949191074967.0_wp q(4,5) = 669434039615170.0_wp/1057158347774751.0_wp q(4,6) = 54695071619813.0_wp/360552159189267.0_wp q(5,1) = -230710230655238.0_wp/986862058648855.0_wp q(5,2) = -612226935261785.0_wp/908213414591054.0_wp q(5,3) = -348257041186489.0_wp/826711871006912.0_wp q(5,4) = -547387049924383.0_wp/1004333317737870.0_wp q(5,5) = -93757604887025.0_wp/1258295855286277.0_wp q(5,6) = 169864933909004.0_wp/1628948931675769.0_wp q(6,1) = -155736850076463.0_wp/183587831567999.0_wp q(6,2) = 451612229494340.0_wp/1497024344481031.0_wp q(6,3) = 125997754350593.0_wp/913954442321314.0_wp q(6,4) = -43892636866549.0_wp/594611800774485.0_wp q(6,5) = -871536553433881.0_wp/2175635418930201.0_wp q(6,6) = -79621653696938.0_wp/1192157037806237.0_wp ! ======= t(1,1) = 19.0_wp/100.0_wp t(1,2) = 541612464959981.0_wp/1297740562774416.0_wp t(1,3) = 1020573445252863.0_wp/1302372457536010.0_wp t(1,4) = 1050875675766104.0_wp/964563697304705.0_wp t(1,5) = 1877996302499711.0_wp/2330793925562261.0_wp t(1,6) = 3815096741193031.0_wp/1649774300229087.0_wp t(2,1) = 0.0_wp/1.0_wp t(2,2) = 19.0_wp/100.0_wp t(2,3) = 285223740406765.0_wp/584945537372783.0_wp t(2,4) = 186799839264170.0_wp/362379195243379.0_wp t(2,5) = 364652677802843.0_wp/699384593799095.0_wp t(2,6) = 1633178268362047.0_wp/1105700192257792.0_wp t(3,1) = 0.0_wp/1.0_wp t(3,2) = 0.0_wp/1.0_wp t(3,3) = 19.0_wp/100.0_wp t(3,4) = 461266320773551.0_wp/1142118708204274.0_wp t(3,5) = 194323258852757.0_wp/1197611677570857.0_wp t(3,6) = 1130557593216792.0_wp/681788337143461.0_wp t(4,1) = 0.0_wp/1.0_wp t(4,2) = 0.0_wp/1.0_wp t(4,3) = 0.0_wp/1.0_wp t(4,4) = 19.0_wp/100.0_wp t(4,5) = 28100770323423.0_wp/369484032261041.0_wp t(4,6) = -152370522143235.0_wp/110528887699756.0_wp t(5,1) = 0.0_wp/1.0_wp t(5,2) = 0.0_wp/1.0_wp t(5,3) = 0.0_wp/1.0_wp t(5,4) = 0.0_wp/1.0_wp t(5,5) = 19.0_wp/100.0_wp t(5,6) = 612877213228136.0_wp/553898027906807.0_wp t(6,1) = 0.0_wp/1.0_wp t(6,2) = 0.0_wp/1.0_wp t(6,3) = 0.0_wp/1.0_wp t(6,4) = 0.0_wp/1.0_wp t(6,5) = 0.0_wp/1.0_wp t(6,6) = 19.0_wp/100.0_wp !===================================================================================================================120 !===================================================================================================================120 ! ********************* SIRK5(4)6L[4]SA ********************* !===================================================================================================================120 !===================================================================================================================120 ! ! SIRK, 6-stage, order =5, stage-order = 4, ! Stiffly-accurate, internally L-stable on ALL stages ! ! D = 1.25785 ! Min{a,b} = {-1.25785, -0.5725} ! Max{a,b} = {1.17543, 0.819953} ! {Min.,Max} Eig(M), = {-0.0934057, 1.97393} ! Cmeasure = 0.305892 ! {Min., Max., RMS} Eig(M)int = {-0.274801, -0.141709, 0.432538} ! Condition Number of S, kappa(S)_{2,Inf} = {5699.84, 8323.97} ! ! 386 242 105 519 802 ! c = {----, ---, ---, ---, ---, 1}, ! 1809 425 337 793 961 ! ! g = 23/125 ! ! {A1,A2,A3,A4,A5,A6,A7} = {0, 0, 0, 0, 0, 0.00079673374, 0.0022258129} ! Embedded method ! {A1h,A2h,A3h,A4h,A5h,A6h,A7h} = {0, 0, 0, 0, 0.0010530385, 0.0029187202, 0.0047491680} ! B,C,E = {2.772, 2.055, 0.7566} !============================================================== !===================================================================================================================120 casename='SIRK5[4]6L[4]SA ' ! SIRK5(4)6L[4]SA !===================================================================================================================120 ns = 6 aI(1,1) = 276962354096155.0_wp/310042368383017.0_wp aI(2,1) = 829435706824353.0_wp/705647422294547.0_wp aI(3,1) = 1155048223015395.0_wp/1173332741338939.0_wp aI(4,1) = 583997751728484.0_wp/702125335017143.0_wp aI(5,1) = 944505387630485.0_wp/908449391984093.0_wp aI(6,1) = 624473784440231.0_wp/761596737518277.0_wp aI(1,2) = 487922857655662.0_wp/1417528413635365.0_wp aI(2,2) = 1188779244889388.0_wp/1165055284845815.0_wp aI(3,2) = 407347413874943.0_wp/1118021450334608.0_wp aI(4,2) = 277568820680765.0_wp/864344466785424.0_wp aI(5,2) = 804517633531877.0_wp/876139915036949.0_wp aI(6,2) = 171873571350442.0_wp/755141847561719.0_wp aI(1,3) = -1275518769180729.0_wp/1333097314890362.0_wp aI(2,3) = -3346166099863205.0_wp/2660227656848502.0_wp aI(3,3) = -449018487193627.0_wp/455939791559625.0_wp aI(4,3) = -206515848429042.0_wp/344159971307021.0_wp aI(5,3) = -284717749297916.0_wp/281325738061557.0_wp aI(6,3) = -452297413754756.0_wp/790038882788739.0_wp aI(1,4) = 96036017665733.0_wp/725134278339489.0_wp aI(2,4) = 5184261417995.0_wp/236313322494113.0_wp aI(3,4) = 207511817161525.0_wp/991988059685181.0_wp aI(4,4) = 332702663616837.0_wp/1051209857378648.0_wp aI(5,4) = 48294411671209.0_wp/1042694629153382.0_wp aI(6,4) = 315838954947561.0_wp/653089604402989.0_wp aI(1,5) = -547747175261128.0_wp/1913554197835981.0_wp aI(2,5) = -600422899632515.0_wp/1010417486336011.0_wp aI(3,5) = -298767041617331.0_wp/790704276770661.0_wp aI(4,5) = -185855598979876.0_wp/633921816372771.0_wp aI(5,5) = -199870997724822.0_wp/715861967753219.0_wp aI(6,5) = -108196917644231.0_wp/1120920833102201.0_wp aI(1,6) = 81994499371270.0_wp/948117029494929.0_wp aI(2,6) = 241540214047847.0_wp/1185370876464130.0_wp aI(3,6) = 116120241232955.0_wp/998535280258039.0_wp aI(4,6) = 77298443819223.0_wp/986781812931221.0_wp aI(5,6) = 97241005810263.0_wp/800015806449134.0_wp aI(6,6) = 147494140982767.0_wp/1069882318456709.0_wp !================================================================ bE(1) = 624473784440231.0_wp/761596737518277.0_wp bE(2) = 171873571350442.0_wp/755141847561719.0_wp bE(3) = -452297413754756.0_wp/790038882788739.0_wp bE(4) = 315838954947561.0_wp/653089604402989.0_wp bE(5) = -108196917644231.0_wp/1120920833102201.0_wp bE(6) = 147494140982767.0_wp/1069882318456709.0_wp !================================================================ bEh(1) = 2406303879626438.0_wp/2513932861617879.0_wp bEh(2) = 381935975066630.0_wp/1180159275804439.0_wp bEh(3) = -769378513179247.0_wp/938678136827297.0_wp bEh(4) = 385731786567940.0_wp/584666589430579.0_wp bEh(5) = -1117420603294271.0_wp/3301936476765577.0_wp bEh(6) = 258578331636886.0_wp/1188922524452835.0_wp !================================================================ cE(1) = 386.0_wp/1809.0_wp cE(2) = 242.0_wp/425.0_wp cE(3) = 105.0_wp/337.0_wp cE(4) = 519.0_wp/793.0_wp cE(5) = 802.0_wp/961.0_wp cE(6) = 1.0_wp/1.0_wp !================================================================ g = 23.0_wp/125.0_wp !================================================================ s(1,1) = 361546174681847.0_wp/772070215576993.0_wp s(2,1) = 342555838412822.0_wp/1130844917755401.0_wp s(3,1) = -3372854965521.0_wp/516928401842377.0_wp s(4,1) = -43186925485747.0_wp/600901128847053.0_wp s(5,1) = 1855380962155227.0_wp/708195557310580.0_wp s(6,1) = 3663.0_wp/1000.0_wp s(1,2) = -682478202019348.0_wp/847041653148777.0_wp s(2,2) = 8601371834074601.0_wp/972463225435366.0_wp s(3,2) = -158223817187048.0_wp/422135316836495.0_wp s(4,2) = 6387090508471499.0_wp/912716868403381.0_wp s(5,2) = 8100592089426067.0_wp/663352800281648.0_wp s(6,2) = 19.0_wp/8.0_wp s(1,3) = 5427925424030651.0_wp/229669944237809.0_wp s(2,3) = 1981009495899103.0_wp/152627855429126.0_wp s(3,3) = 8463252433420206.0_wp/566110132227301.0_wp s(4,3) = -9996733622555059.0_wp/499134320394571.0_wp s(5,3) = 27914616744492453.0_wp/1572896232131815.0_wp s(6,3) = 0.0_wp/1.0_wp s(1,4) = -90748521686633363.0_wp/908096435993956.0_wp s(2,4) = 77249743051555532.0_wp/1225587782054795.0_wp s(3,4) = -58591493595427532.0_wp/711935548175669.0_wp s(4,4) = 46170134078336023.0_wp/823640532656768.0_wp s(5,4) = 28298758009456272.0_wp/512874789863989.0_wp s(6,4) = 2829.0_wp/100.0_wp s(1,5) = -355219595449276218.0_wp/1540425438362759.0_wp s(2,5) = 162841163816888433.0_wp/1234423801868107.0_wp s(3,5) = 1532210089736347319.0_wp/3051691843463469.0_wp s(4,5) = 1000724194489031909.0_wp/1378148235731517.0_wp s(5,5) = -1062590983218389318.0_wp/782767342636349.0_wp s(6,5) = 16053.0_wp/100.0_wp s(1,6) = -2278166524415233239.0_wp/861741434728967.0_wp s(2,6) = -2108360746291803983.0_wp/451696204104997.0_wp s(3,6) = 2157014831561386597.0_wp/734595399311860.0_wp s(4,6) = 4953910884295763548.0_wp/718283008597231.0_wp s(5,6) = -18175286019022008150.0_wp/1010620299736207.0_wp s(6,6) = -29.0_wp/4.0_wp ! ======= sinv(1,1) = 20371628100689.0_wp/624298878188762.0_wp sinv(2,1) = 146970549939537.0_wp/989863648610711.0_wp sinv(3,1) = 146909365802959.0_wp/1089395347351870.0_wp sinv(4,1) = 6481220981131.0_wp/431075584400260.0_wp sinv(5,1) = -4723017606545.0_wp/849611971032582.0_wp sinv(6,1) = 410243334790.0_wp/582418388665129.0_wp sinv(1,2) = -27685221599546.0_wp/345551679521617.0_wp sinv(2,2) = 8556307836541.0_wp/734114124000444.0_wp sinv(3,2) = 84050113738479.0_wp/1100630446073971.0_wp sinv(4,2) = 10609678821947.0_wp/717412606818225.0_wp sinv(5,2) = -556206983954.0_wp/590459631210263.0_wp sinv(6,2) = 212045147395.0_wp/1127435903195831.0_wp sinv(1,3) = -3735963187232.0_wp/624705392592429.0_wp sinv(2,3) = -81891101493179.0_wp/972807965487394.0_wp sinv(3,3) = -119061991219693.0_wp/895414839393800.0_wp sinv(4,3) = -23271806684228.0_wp/911392093896947.0_wp sinv(5,3) = 3577680887113.0_wp/611596106809592.0_wp sinv(6,3) = -1318080106603.0_wp/1858716095712388.0_wp sinv(1,4) = -794610141803.0_wp/112452149464025.0_wp sinv(2,4) = 41837586708522.0_wp/322173531590039.0_wp sinv(3,4) = 9947215870560.0_wp/1296878557506473.0_wp sinv(4,4) = -1012069570153.0_wp/845971271536057.0_wp sinv(5,4) = -1419626529764.0_wp/921941510385717.0_wp sinv(6,4) = 547117366269.0_wp/2639580603088984.0_wp sinv(1,5) = 9050033849975.0_wp/741587386564071.0_wp sinv(2,5) = 8790910126359.0_wp/783782433709409.0_wp sinv(3,5) = -52240648718504.0_wp/894236531513507.0_wp sinv(4,5) = -3160855276954.0_wp/296014328997497.0_wp sinv(5,5) = 1056859935878.0_wp/740956828789799.0_wp sinv(6,5) = -295028843770.0_wp/1207732658693779.0_wp sinv(1,6) = 1138999864279795.0_wp/4272691537121674.0_wp sinv(2,6) = -32570001308399.0_wp/1273803105537900.0_wp sinv(3,6) = 17601819351627.0_wp/970251307428124.0_wp sinv(4,6) = 2000770951048.0_wp/452338500628909.0_wp sinv(5,6) = -165067580105.0_wp/656648932240079.0_wp sinv(6,6) = 164357624253.0_wp/2285306684327143.0_wp ! ======= jcf(1,1) = 23.0_wp/125.0_wp jcf(2,1) = 0.0_wp/1.0_wp jcf(3,1) = 0.0_wp/1.0_wp jcf(4,1) = 0.0_wp/1.0_wp jcf(5,1) = 0.0_wp/1.0_wp jcf(6,1) = 0.0_wp/1.0_wp jcf(1,2) = 1.0_wp/1.0_wp jcf(2,2) = 23.0_wp/125.0_wp jcf(3,2) = 0.0_wp/1.0_wp jcf(4,2) = 0.0_wp/1.0_wp jcf(5,2) = 0.0_wp/1.0_wp jcf(6,2) = 0.0_wp/1.0_wp jcf(1,3) = 0.0_wp/1.0_wp jcf(2,3) = 1.0_wp/1.0_wp jcf(3,3) = 23.0_wp/125.0_wp jcf(4,3) = 0.0_wp/1.0_wp jcf(5,3) = 0.0_wp/1.0_wp jcf(6,3) = 0.0_wp/1.0_wp jcf(1,4) = 0.0_wp/1.0_wp jcf(2,4) = 0.0_wp/1.0_wp jcf(3,4) = 1.0_wp/1.0_wp jcf(4,4) = 23.0_wp/125.0_wp jcf(5,4) = 0.0_wp/1.0_wp jcf(6,4) = 0.0_wp/1.0_wp jcf(1,5) = 0.0_wp/1.0_wp jcf(2,5) = 0.0_wp/1.0_wp jcf(3,5) = 0.0_wp/1.0_wp jcf(4,5) = 1.0_wp/1.0_wp jcf(5,5) = 23.0_wp/125.0_wp jcf(6,5) = 0.0_wp/1.0_wp jcf(1,6) = 0.0_wp/1.0_wp jcf(2,6) = 0.0_wp/1.0_wp jcf(3,6) = 0.0_wp/1.0_wp jcf(4,6) = 0.0_wp/1.0_wp jcf(5,6) = 1.0_wp/1.0_wp jcf(6,6) = 23.0_wp/125.0_wp ! ======= q(1,1) = 93085057377297.0_wp/902154188653397.0_wp q(1,2) = -110447692322226.0_wp/870674182003949.0_wp q(1,3) = 442846915017740.0_wp/752671681658499.0_wp q(1,4) = 75392307281987.0_wp/173598924861978.0_wp q(1,5) = -80684109040097.0_wp/1260156056429965.0_wp q(1,6) = 245425289515553.0_wp/372378643891501.0_wp q(2,1) = 49896595153633.0_wp/747567407989385.0_wp q(2,2) = 539635605507040.0_wp/916950195212273.0_wp q(2,3) = 670090752612866.0_wp/2446783278066307.0_wp q(2,4) = -248001809806737.0_wp/636173295787714.0_wp q(2,5) = 392445758246698.0_wp/627405564351831.0_wp q(2,6) = 141355756928693.0_wp/803246667603136.0_wp q(3,1) = -457274197401.0_wp/318065961766304.0_wp q(3,2) = -32078644101685.0_wp/1239927644444734.0_wp q(3,3) = 745028921922049.0_wp/1898069598424479.0_wp q(3,4) = 507247767583448.0_wp/972303064691563.0_wp q(3,5) = 532512995563031.0_wp/1461136152222872.0_wp q(3,6) = -86075207376872.0_wp/129724271783755.0_wp q(4,1) = -11455592695513.0_wp/723395940836827.0_wp q(4,2) = 1751020667785910.0_wp/3422433254783819.0_wp q(4,3) = -144028280243683.0_wp/260687842460082.0_wp q(4,4) = 183152481794465.0_wp/294751578588417.0_wp q(4,5) = 36708742708681.0_wp/386751569881852.0_wp q(4,6) = 194107556966138.0_wp/1000849510621723.0_wp q(5,1) = 440952433816431.0_wp/763870286799206.0_wp q(5,2) = 441210737907239.0_wp/905376938602781.0_wp q(5,3) = 80441833197995.0_wp/364256796685076.0_wp q(5,4) = -37016301765272.0_wp/1176748438604211.0_wp q(5,5) = -930613023350343.0_wp/1626700836501239.0_wp q(5,6) = -192781561265165.0_wp/843419690017493.0_wp q(6,1) = 348221841608208.0_wp/431446410793255.0_wp q(6,2) = -116531309005183.0_wp/314096758674760.0_wp q(6,3) = -182567114576284.0_wp/686457231521017.0_wp q(6,4) = 22442368419909.0_wp/1819010042397988.0_wp q(6,5) = 432126518626593.0_wp/1173811164741013.0_wp q(6,6) = 62854521705062.0_wp/934034827640527.0_wp ! ======= t(1,1) = 23.0_wp/125.0_wp t(1,2) = 280153706118370.0_wp/862194180039583.0_wp t(1,3) = 244789826831938.0_wp/1103321436894925.0_wp t(1,4) = -28249166893712.0_wp/480378508780797.0_wp t(1,5) = 21356760420602.0_wp/81657294340119.0_wp t(1,6) = 2252737661337764.0_wp/1098185455283739.0_wp t(2,1) = 0.0_wp/1.0_wp t(2,2) = 23.0_wp/125.0_wp t(2,3) = 364546497241940.0_wp/999949674675921.0_wp t(2,4) = -540359343901279.0_wp/1068701797803337.0_wp t(2,5) = 698579841456329.0_wp/1295223148546519.0_wp t(2,6) = 1927633429322669.0_wp/1021316712593729.0_wp t(3,1) = 0.0_wp/1.0_wp t(3,2) = 0.0_wp/1.0_wp t(3,3) = 23.0_wp/125.0_wp t(3,4) = -470535341922090.0_wp/951334059221587.0_wp t(3,5) = 140200076057965.0_wp/831816669645383.0_wp t(3,6) = 1557911376361741.0_wp/1136788267111079.0_wp t(4,1) = 0.0_wp/1.0_wp t(4,2) = 0.0_wp/1.0_wp t(4,3) = 0.0_wp/1.0_wp t(4,4) = 23.0_wp/125.0_wp t(4,5) = -81057255552664.0_wp/1239891286409623.0_wp t(4,6) = 904833979884418.0_wp/698752979682603.0_wp t(5,1) = 0.0_wp/1.0_wp t(5,2) = 0.0_wp/1.0_wp t(5,3) = 0.0_wp/1.0_wp t(5,4) = 0.0_wp/1.0_wp t(5,5) = 23.0_wp/125.0_wp t(5,6) = 3423862561732266.0_wp/2703772862913223.0_wp t(6,1) = 0.0_wp/1.0_wp t(6,2) = 0.0_wp/1.0_wp t(6,3) = 0.0_wp/1.0_wp t(6,4) = 0.0_wp/1.0_wp t(6,5) = 0.0_wp/1.0_wp t(6,6) = 23.0_wp/125.0_wp !===================================================================================================================120 !===================================================================================================================120 ! ********************* SIRK5(4)7L[4]SA ********************* !===================================================================================================================120 !===================================================================================================================120 ! ! SIRK, 7-stage, order =5, stage-order = 4, ! Stiffly-accurate, internally L-stable on ALL stages ! ! D = 0.535326 ! Min{a,b} = {-0.478249, -0.478249} ! Max{a,b} = {0.535326, 0.531641} ! {Min.,Max} Eig(M), = {-0.154344, 0.489854} ! Cmeasure = 0.26365 ! {Min., Max., RMS} Eig(M)int = {-0.11081, -0.0541887, 0.204658} ! Condition Number of S, kappaI(S)_{2,Inf} = {14493., 16226.4} ! ! 11 47 55 85 41 161 ! c = {--, ---, ---, ---, --, ---, 1}, ! 67 180 119 127 43 193 ! ! g = 1/7 ! ! {A1,A2,A3,A4,A5,A6,A7} = {0, 0, 0, 0, 0, 0.00071780749, 0.0019364272} ! Embedded method ! {A1,A2,A3,A4,A5,A6,A7} = {0, 0, 0, 0, 0.00088455231, 0.0021600087, 0.0032957773} ! B,C,E = {2.4419, 3.25114, 0.811492} !============================================================== !===================================================================================================================120 casename='SIRK5[4]7L[4]SA ' ! SIRK5(4)7L[4]SA !===================================================================================================================120 ns = 7 aI(1,1) = 582245450361074.0_wp/1208758455789599.0_wp aI(2,1) = 206221629094637.0_wp/385225919113430.0_wp aI(3,1) = 799974631724624.0_wp/1502890033042705.0_wp aI(4,1) = 297285246922069.0_wp/720102109519750.0_wp aI(5,1) = 682966354392994.0_wp/1483657888287899.0_wp aI(6,1) = 537424291980239.0_wp/1324745321882355.0_wp aI(7,1) = 297743072816555.0_wp/789845569649653.0_wp aI(1,2) = -243429299008671.0_wp/602266063145477.0_wp aI(2,2) = -209432948387219.0_wp/570939085468559.0_wp aI(3,2) = -255637748505395.0_wp/856190148599299.0_wp aI(4,2) = -11509730061167.0_wp/549009586327029.0_wp aI(5,2) = -196053728397509.0_wp/1479287288391776.0_wp aI(6,2) = -12178239934966.0_wp/1242512696334751.0_wp aI(7,2) = 56609825977467.0_wp/1084573844009858.0_wp aI(1,3) = 24402457342270.0_wp/746294201193267.0_wp aI(2,3) = 18157175144536.0_wp/458426028171763.0_wp aI(3,3) = 866968324675276.0_wp/3557567952575069.0_wp aI(4,3) = -59123198851172.0_wp/2628167462108675.0_wp aI(5,3) = 223359485336592.0_wp/1826000494224475.0_wp aI(6,3) = -9237481276157.0_wp/570249798578157.0_wp aI(7,3) = -87555961211227.0_wp/1214612266615875.0_wp aI(1,4) = 43571412442966.0_wp/325537679839697.0_wp aI(2,4) = 100535424915499.0_wp/764945899663129.0_wp aI(3,4) = 41607173131916.0_wp/1791079395339627.0_wp aI(4,4) = 534332011655153.0_wp/1021753668537666.0_wp aI(5,4) = 514913264507261.0_wp/1239406634480537.0_wp aI(6,4) = 850898184028364.0_wp/1597254697458717.0_wp aI(7,4) = 221980066313075.0_wp/417537501414289.0_wp aI(1,5) = -168848407513680.0_wp/737157299180749.0_wp aI(2,5) = -184531833740884.0_wp/612329994724739.0_wp aI(3,5) = -36137249733531.0_wp/229632872524766.0_wp aI(4,5) = -242134056652609.0_wp/1215274077324624.0_wp aI(5,5) = -285150266115772.0_wp/889667685750017.0_wp aI(6,5) = -388372610642494.0_wp/919814860853569.0_wp aI(7,5) = -322657284369505.0_wp/674663436187378.0_wp aI(1,6) = -20916883459178.0_wp/779593068240793.0_wp aI(2,6) = -695306758769.0_wp/928979827129520.0_wp aI(3,6) = -1759572345831.0_wp/871489428601909.0_wp aI(4,6) = -376348967826533.0_wp/1741444920758171.0_wp aI(5,6) = 141885744633556.0_wp/987503761583197.0_wp aI(6,6) = 21519123483768.0_wp/541119409166693.0_wp aI(7,6) = 229561562374607.0_wp/1206257839104655.0_wp aI(1,7) = 66135590161502.0_wp/375726509921817.0_wp aI(2,7) = 138316838063853.0_wp/618371196048044.0_wp aI(3,7) = 113588619802143.0_wp/939280713455987.0_wp aI(4,7) = 270537571749202.0_wp/1406750621289951.0_wp aI(5,7) = 415831337143299.0_wp/1570634228061452.0_wp aI(6,7) = 326502310783548.0_wp/1073131607505529.0_wp aI(7,7) = 237114614160652.0_wp/593936141003489.0_wp ! ======= bE(1) = 297743072816555.0_wp/789845569649653.0_wp bE(2) = 56609825977467.0_wp/1084573844009858.0_wp bE(3) = -87555961211227.0_wp/1214612266615875.0_wp bE(4) = 221980066313075.0_wp/417537501414289.0_wp bE(5) = -322657284369505.0_wp/674663436187378.0_wp bE(6) = 229561562374607.0_wp/1206257839104655.0_wp bE(7) = 237114614160652.0_wp/593936141003489.0_wp ! ======= bEh(1) = 341628971014197.0_wp/470298835699016.0_wp bEh(2) = -992264775188544.0_wp/1167778517259859.0_wp bEh(3) = 1244030178759544.0_wp/966426844377631.0_wp bEh(4) = -1731380430865750.0_wp/1740391974739577.0_wp bEh(5) = -27775117826363.0_wp/1060856862895032.0_wp bEh(6) = 878885009166788.0_wp/918790350111783.0_wp bEh(7) = -92867194051835.0_wp/933187118757357.0_wp ! ======= cE(1) = 11.0_wp/67.0_wp cE(2) = 47.0_wp/180.0_wp cE(3) = 55.0_wp/119.0_wp cE(4) = 85.0_wp/127.0_wp cE(5) = 41.0_wp/43.0_wp cE(6) = 161.0_wp/193.0_wp cE(7) = 1.0_wp/1.0_wp ! ======= g = 1.0_wp/7.0_wp ! ======= s(1,1) = -1320286982057.0_wp/1969919308324656.0_wp s(2,1) = 985263093482.0_wp/620863946460135.0_wp s(3,1) = 1148127945413.0_wp/756873385391914.0_wp s(4,1) = 2561649848494.0_wp/1782899429175641.0_wp s(5,1) = 46712106365391.0_wp/1540655774306534.0_wp s(6,1) = 5193856411189.0_wp/398713895639072.0_wp s(7,1) = 9.0_wp/200.0_wp s(1,2) = 21566396843044.0_wp/997508615151673.0_wp s(2,2) = 540888611864.0_wp/402033758279045.0_wp s(3,2) = -10428894036809.0_wp/1136688307679442.0_wp s(4,2) = 84252192872275.0_wp/1001277483905866.0_wp s(5,2) = 6068317521996.0_wp/859819235218923.0_wp s(6,2) = 302099949093458.0_wp/2439988320946041.0_wp s(7,2) = 3.0_wp/500.0_wp s(1,3) = -208703640911667.0_wp/1297246869791084.0_wp s(2,3) = 54558646221782.0_wp/599075190869077.0_wp s(3,3) = 327025430948809.0_wp/842320903775858.0_wp s(4,3) = -101495078564954.0_wp/2502970189366571.0_wp s(5,3) = -732067970855576.0_wp/1839483982836513.0_wp s(6,3) = -437482700228057.0_wp/1003153134850924.0_wp s(7,3) = 2.0_wp/125.0_wp s(1,4) = 993167018037989.0_wp/458029445732608.0_wp s(2,4) = 165723647541081.0_wp/282284668224547.0_wp s(3,4) = -3286750651553373.0_wp/1183063193857411.0_wp s(4,4) = -545245983786265.0_wp/673998346091526.0_wp s(5,4) = 2106051411778369.0_wp/1147623753839897.0_wp s(6,4) = 1093268701586603.0_wp/755366616206166.0_wp s(7,4) = 0.0_wp/1.0_wp s(1,5) = -12565407562668863.0_wp/821053699864947.0_wp s(2,5) = -4827370875705293.0_wp/418195339989691.0_wp s(3,5) = 12057236510665529.0_wp/1032644676486508.0_wp s(4,5) = 15509834097812516.0_wp/1336460667011619.0_wp s(5,5) = -1992729707904647.0_wp/527112320656534.0_wp s(6,5) = -695002751449517.0_wp/265635582958474.0_wp s(7,5) = -26.0_wp/25.0_wp s(1,6) = 40301693378191515.0_wp/534879638314528.0_wp s(2,6) = 27110860162945613.0_wp/459715615966367.0_wp s(3,6) = 11379623508419444.0_wp/1567248137092539.0_wp s(4,6) = -4744193267645330.0_wp/2961718728622983.0_wp s(5,6) = 39867313675441028.0_wp/653717974564601.0_wp s(6,6) = 15353313272499157.0_wp/1428808342719856.0_wp s(7,6) = -157.0_wp/10.0_wp s(1,7) = -214117802323057971.0_wp/1139309891222081.0_wp s(2,7) = -375983762703272063.0_wp/1107149442527013.0_wp s(3,7) = 463115831932148683.0_wp/1194534285437742.0_wp s(4,7) = 240560402017757463.0_wp/622035873568063.0_wp s(5,7) = 244732814041162827.0_wp/1369981898356151.0_wp s(6,7) = 74081012808880469.0_wp/1377455749563000.0_wp s(7,7) = -577.0_wp/5.0_wp ! ======= sinv(1,1) = -517697125690055.0_wp/1215258141578321.0_wp sinv(2,1) = 10579554527100464.0_wp/1243878372221651.0_wp sinv(3,1) = 3274356283164304.0_wp/503773411454717.0_wp sinv(4,1) = 1221252783592790.0_wp/1320352686876869.0_wp sinv(5,1) = -128100514449549.0_wp/883914615908635.0_wp sinv(6,1) = -25323868385021.0_wp/1348373007797882.0_wp sinv(7,1) = 5496981723701.0_wp/1091000978066929.0_wp sinv(1,2) = -1344297952126936.0_wp/772363841936213.0_wp sinv(2,2) = 295245220918507.0_wp/988951427384716.0_wp sinv(3,2) = -1784517622281869.0_wp/812218140617304.0_wp sinv(4,2) = -111756582671533.0_wp/284252985381040.0_wp sinv(5,2) = 126676608075615.0_wp/923624630925748.0_wp sinv(6,2) = 34579052735189.0_wp/1603515055714377.0_wp sinv(7,2) = -4126644403901.0_wp/803215446276080.0_wp sinv(1,3) = 3561259717657133.0_wp/1255529575052228.0_wp sinv(2,3) = -119098730938066.0_wp/787963041057491.0_wp sinv(3,3) = -1138434052190135.0_wp/692555247409234.0_wp sinv(4,3) = -1058147625718925.0_wp/1200550596228993.0_wp sinv(5,3) = -127720807005008.0_wp/780009345796519.0_wp sinv(6,3) = -4249644946033.0_wp/1037973197743320.0_wp sinv(7,3) = 7490361144289.0_wp/2580233329958628.0_wp sinv(1,4) = -1779090454318655.0_wp/924205541669889.0_wp sinv(2,4) = 2131477595955348.0_wp/212849592429455.0_wp sinv(3,4) = 4971302338942527.0_wp/788968328772265.0_wp sinv(4,4) = 713354727232528.0_wp/499681473979715.0_wp sinv(5,4) = 351804395540707.0_wp/1880283895363377.0_wp sinv(6,4) = 2742407101312.0_wp/752405581557423.0_wp sinv(7,4) = -1696609555225.0_wp/1102821274261351.0_wp sinv(1,5) = 9784113591057984.0_wp/1368900350895563.0_wp sinv(2,5) = -8747558120312617.0_wp/862960406748571.0_wp sinv(3,5) = -1713092568023741.0_wp/429670886111616.0_wp sinv(4,5) = -154288717145746.0_wp/510085650016047.0_wp sinv(5,5) = 61217290944709.0_wp/646495459890688.0_wp sinv(6,5) = 13135189212703.0_wp/717278358925565.0_wp sinv(7,5) = -3070241133956.0_wp/1874998369208233.0_wp sinv(1,6) = -2923128528305395.0_wp/872659012094762.0_wp sinv(2,6) = 5114053939690263.0_wp/965569896462173.0_wp sinv(3,6) = -3323801815098868.0_wp/970589633797353.0_wp sinv(4,6) = -1008228241997083.0_wp/964194883798024.0_wp sinv(5,6) = -97312804461419.0_wp/578203741297594.0_wp sinv(6,6) = -9447025484204.0_wp/978875970389501.0_wp sinv(7,6) = 1514959649075.0_wp/1144124796845656.0_wp sinv(1,7) = 8400966615437027.0_wp/456647609744458.0_wp sinv(2,7) = 2387725451040287.0_wp/468355649976363.0_wp sinv(3,7) = 2531514159711689.0_wp/683057770393136.0_wp sinv(4,7) = 292441437466570.0_wp/564267327512989.0_wp sinv(5,7) = -20053655537467.0_wp/890108568804858.0_wp sinv(6,7) = -2702740592674.0_wp/255862275078337.0_wp sinv(7,7) = 977118308150.0_wp/1053551993947271.0_wp ! ======= jcf(1,1) = 1.0_wp/7.0_wp jcf(2,1) = 0.0_wp/1.0_wp jcf(3,1) = 0.0_wp/1.0_wp jcf(4,1) = 0.0_wp/1.0_wp jcf(5,1) = 0.0_wp/1.0_wp jcf(6,1) = 0.0_wp/1.0_wp jcf(7,1) = 0.0_wp/1.0_wp jcf(1,2) = 1.0_wp/1.0_wp jcf(2,2) = 1.0_wp/7.0_wp jcf(3,2) = 0.0_wp/1.0_wp jcf(4,2) = 0.0_wp/1.0_wp jcf(5,2) = 0.0_wp/1.0_wp jcf(6,2) = 0.0_wp/1.0_wp jcf(7,2) = 0.0_wp/1.0_wp jcf(1,3) = 0.0_wp/1.0_wp jcf(2,3) = 1.0_wp/1.0_wp jcf(3,3) = 1.0_wp/7.0_wp jcf(4,3) = 0.0_wp/1.0_wp jcf(5,3) = 0.0_wp/1.0_wp jcf(6,3) = 0.0_wp/1.0_wp jcf(7,3) = 0.0_wp/1.0_wp jcf(1,4) = 0.0_wp/1.0_wp jcf(2,4) = 0.0_wp/1.0_wp jcf(3,4) = 1.0_wp/1.0_wp jcf(4,4) = 1.0_wp/7.0_wp jcf(5,4) = 0.0_wp/1.0_wp jcf(6,4) = 0.0_wp/1.0_wp jcf(7,4) = 0.0_wp/1.0_wp jcf(1,5) = 0.0_wp/1.0_wp jcf(2,5) = 0.0_wp/1.0_wp jcf(3,5) = 0.0_wp/1.0_wp jcf(4,5) = 1.0_wp/1.0_wp jcf(5,5) = 1.0_wp/7.0_wp jcf(6,5) = 0.0_wp/1.0_wp jcf(7,5) = 0.0_wp/1.0_wp jcf(1,6) = 0.0_wp/1.0_wp jcf(2,6) = 0.0_wp/1.0_wp jcf(3,6) = 0.0_wp/1.0_wp jcf(4,6) = 0.0_wp/1.0_wp jcf(5,6) = 1.0_wp/1.0_wp jcf(6,6) = 1.0_wp/7.0_wp jcf(7,6) = 0.0_wp/1.0_wp jcf(1,7) = 0.0_wp/1.0_wp jcf(2,7) = 0.0_wp/1.0_wp jcf(3,7) = 0.0_wp/1.0_wp jcf(4,7) = 0.0_wp/1.0_wp jcf(5,7) = 0.0_wp/1.0_wp jcf(6,7) = 1.0_wp/1.0_wp jcf(7,7) = 1.0_wp/7.0_wp ! ======= q(1,1) = -79143949497776.0_wp/6597293135409327.0_wp q(1,2) = 130474984521081.0_wp/870542514918359.0_wp q(1,3) = 267025038027697.0_wp/1361974588178466.0_wp q(1,4) = 1170929551857110.0_wp/1658108925886573.0_wp q(1,5) = -129199838789612.0_wp/546494613826139.0_wp q(1,6) = -159721625263033.0_wp/1571700259888291.0_wp q(1,7) = 528250927255038.0_wp/863737415045845.0_wp q(2,1) = 7547932476305.0_wp/265729762280578.0_wp q(2,2) = -5240571286113.0_wp/1053683383589483.0_wp q(2,3) = -706840518482951.0_wp/3480518293339432.0_wp q(2,4) = 393071402973184.0_wp/568373764588179.0_wp q(2,5) = 149286616990684.0_wp/500788156860261.0_wp q(2,6) = -36891274494257.0_wp/851325400019717.0_wp q(2,7) = -336531025976605.0_wp/539635773026214.0_wp q(3,1) = 34216761424778.0_wp/1260200984511017.0_wp q(3,2) = -64696098384827.0_wp/869285572904310.0_wp q(3,3) = -381442463581589.0_wp/504577711338565.0_wp q(3,4) = -44821907137739.0_wp/828751794890150.0_wp q(3,5) = 779595632126698.0_wp/2827201270264505.0_wp q(3,6) = -204029600223707.0_wp/435871703810206.0_wp q(3,7) = 355698684514851.0_wp/1009436722738922.0_wp q(4,1) = 30792661232424.0_wp/1197353176899713.0_wp q(4,2) = 171361318093583.0_wp/312819785993411.0_wp q(4,3) = -1039219411381357.0_wp/2200877468886369.0_wp q(4,4) = -19171316230040.0_wp/1183978315761351.0_wp q(4,5) = -580253645348047.0_wp/899512827202925.0_wp q(4,6) = 73007186478851.0_wp/461327325580023.0_wp q(4,7) = -431467544576877.0_wp/2310531946489091.0_wp q(5,1) = 443831303947880.0_wp/817828162569233.0_wp q(5,2) = 228965748723617.0_wp/1126113060495414.0_wp q(5,3) = 313691103982307.0_wp/1038779267568573.0_wp q(5,4) = -6210595927521.0_wp/65320989738448.0_wp q(5,5) = -364910989347736.0_wp/2586665850095593.0_wp q(5,6) = -658259644666149.0_wp/926757151235177.0_wp q(5,7) = -131223878100139.0_wp/660209690424814.0_wp q(6,1) = 176083781153963.0_wp/755194389326418.0_wp q(6,2) = 233228241507455.0_wp/328388534812423.0_wp q(6,3) = 76563144710980.0_wp/1105130940920959.0_wp q(6,4) = -81743081765592.0_wp/1115688433359613.0_wp q(6,5) = 349533447459320.0_wp/601723583661521.0_wp q(6,6) = 186222587546069.0_wp/715229570865447.0_wp q(6,7) = 143315040522270.0_wp/891671162058119.0_wp q(7,1) = 224239632938026.0_wp/278399099831381.0_wp q(7,2) = -157954323145409.0_wp/444740338453272.0_wp q(7,3) = -111414451406504.0_wp/644465258655767.0_wp q(7,4) = 80414184038887.0_wp/1090515495522176.0_wp q(7,5) = -105016831841324.0_wp/1384794416492543.0_wp q(7,6) = 334537056916499.0_wp/808183176981348.0_wp q(7,7) = 112930784218109.0_wp/1003140545550144.0_wp ! ======= t(1,1) = 1.0_wp/7.0_wp t(1,2) = 963946462417486.0_wp/2590626469443051.0_wp t(1,3) = -512156633358663.0_wp/981126097102370.0_wp t(1,4) = 972362431224769.0_wp/1856937309001882.0_wp t(1,5) = -1196682213820347.0_wp/2420586583462757.0_wp t(1,6) = 717018205382478.0_wp/875203451358017.0_wp t(1,7) = 225637017238526.0_wp/421472734821205.0_wp t(2,1) = 0.0_wp/1.0_wp t(2,2) = 1.0_wp/7.0_wp t(2,3) = -532004394065746.0_wp/1692047695522713.0_wp t(2,4) = 238203628183601.0_wp/710307072667110.0_wp t(2,5) = -743223735871375.0_wp/1307759656689984.0_wp t(2,6) = 398132915401151.0_wp/1176066988559196.0_wp t(2,7) = 328894735130031.0_wp/970054225003862.0_wp t(3,1) = 0.0_wp/1.0_wp t(3,2) = 0.0_wp/1.0_wp t(3,3) = 1.0_wp/7.0_wp t(3,4) = -153295848299271.0_wp/584259457704656.0_wp t(3,5) = 466215056312072.0_wp/1476243362138865.0_wp t(3,6) = -127117094588299.0_wp/1308918691558469.0_wp t(3,7) = -568442752110098.0_wp/1208852034471801.0_wp t(4,1) = 0.0_wp/1.0_wp t(4,2) = 0.0_wp/1.0_wp t(4,3) = 0.0_wp/1.0_wp t(4,4) = 1.0_wp/7.0_wp t(4,5) = -319921294274913.0_wp/878364926223776.0_wp t(4,6) = 428978097006155.0_wp/1408611357947947.0_wp t(4,7) = 831918562133317.0_wp/1075284463521852.0_wp t(5,1) = 0.0_wp/1.0_wp t(5,2) = 0.0_wp/1.0_wp t(5,3) = 0.0_wp/1.0_wp t(5,4) = 0.0_wp/1.0_wp t(5,5) = 1.0_wp/7.0_wp t(5,6) = 102714425623415.0_wp/1251416674878962.0_wp t(5,7) = 457577927646037.0_wp/2534561755234119.0_wp t(6,1) = 0.0_wp/1.0_wp t(6,2) = 0.0_wp/1.0_wp t(6,3) = 0.0_wp/1.0_wp t(6,4) = 0.0_wp/1.0_wp t(6,5) = 0.0_wp/1.0_wp t(6,6) = 1.0_wp/7.0_wp t(6,7) = -329034683043261.0_wp/656003470182002.0_wp t(7,1) = 0.0_wp/1.0_wp t(7,2) = 0.0_wp/1.0_wp t(7,3) = 0.0_wp/1.0_wp t(7,4) = 0.0_wp/1.0_wp t(7,5) = 0.0_wp/1.0_wp t(7,6) = 0.0_wp/1.0_wp t(7,7) = 1.0_wp/7.0_wp !===================================================================================================================120 !===================================================================================================================120 ! ********************* SIRK6(5)7L[4]SA ********************* !===================================================================================================================120 !===================================================================================================================120 ! ! SIRK, 7-stage, order = 6(5), stage-order = 4, ! Stiffly-accurate, internally L-stable on ALL stages ! ! D = 1.51122 ! Min{a,b} = {-1.51122, -1.51122} ! Max{a,b} = {1.38083, 1.38083} ! {Min.,Max} Eig(M), = {-1.77214, 2.43224} ! Cmeasure = 0.251977 ! {Min., Max., RMS} Eig(M)int = {-1.65123, -0.5292, 3.16267} ! Condition Number of A, kappa(A)_{2} = {2.16847} thousand ! Condition Number of S, kappa(S)_{2,Inf} = {38989.9, 67151.} ! ! 315 160 901 312 220 1071 ! c = {----, ---, ----, ---, ---, ----, 1}, ! 1478 563 2075 457 427 1142 ! ! g = 2041/10000 ! ! {A1 ,A2 ,A3 ,A4 ,A5 ,A6 ,A7 } = {0, 0, 0, 0, 0, 0, 0.00035945032} ! Embedded method ! {A1h,A2h,A3h,A4h,A5h,A6h} = {0., 0., 0., 0., 0., 0.000715315} ! B,C,E = {3.043, 3.019, 0.5025} !============================================================== !===================================================================================================================120 casename='SIRK6[5]7L[4]SA ' ! SIRK6(5)7L[4]SA !===================================================================================================================120 ns = 7 aI(1,1) = 1393106712015778.0_wp/1445042073773939.0_wp aI(2,1) = 657279807271213.0_wp/563144535926102.0_wp aI(3,1) = 633625582266259.0_wp/622344297574402.0_wp aI(4,1) = 79322745815537.0_wp/115270876430830.0_wp aI(5,1) = 1152798092030275.0_wp/937374120436764.0_wp aI(6,1) = 998900237373849.0_wp/920242077096968.0_wp aI(7,1) = 342058879474588.0_wp/247719565460375.0_wp aI(1,2) = -829745190667821.0_wp/978492644573104.0_wp aI(2,2) = -871492134525669.0_wp/764687277038030.0_wp aI(3,2) = -861367584263665.0_wp/1013402605528803.0_wp aI(4,2) = -118981346613409.0_wp/1227289904602060.0_wp aI(5,2) = -588913599387299.0_wp/486931553494149.0_wp aI(6,2) = -580617012750148.0_wp/684312903316221.0_wp aI(7,2) = -1242156892003476.0_wp/821956816784831.0_wp aI(1,3) = -181494282254396.0_wp/648021299404851.0_wp aI(2,3) = -126413258322727.0_wp/873236653864028.0_wp aI(3,3) = 290889396023063.0_wp/953355173438137.0_wp aI(4,3) = -768105323264493.0_wp/1085437422005587.0_wp aI(5,3) = 4115892676536.0_wp/1169448456997793.0_wp aI(6,3) = -494142487075212.0_wp/764205231261569.0_wp aI(7,3) = 47996106307509.0_wp/613169560650038.0_wp aI(1,4) = 136876985590598.0_wp/1199760291836705.0_wp aI(2,4) = -32845967863247.0_wp/257134833027264.0_wp aI(3,4) = 102009195350375.0_wp/264592829995152.0_wp aI(4,4) = 363861002133521.0_wp/684403406951518.0_wp aI(5,4) = -500859026911441.0_wp/1367313200818842.0_wp aI(6,4) = -311519184031744.0_wp/1775473955788955.0_wp aI(7,4) = -513370256818603.0_wp/1083398076347323.0_wp aI(1,5) = 430601419500463.0_wp/1150785430053135.0_wp aI(2,5) = 550995289209196.0_wp/980198786220721.0_wp aI(3,5) = -116613582929960.0_wp/485377633468273.0_wp aI(4,5) = 320325834313071.0_wp/617501905928725.0_wp aI(5,5) = 298131089873929.0_wp/370635840689801.0_wp aI(6,5) = 1293589847415290.0_wp/950841728087699.0_wp aI(7,5) = 461378680164967.0_wp/397240231852477.0_wp aI(1,6) = -72659588954263.0_wp/222344814508863.0_wp aI(2,6) = -88653640579347.0_wp/620404970520319.0_wp aI(3,6) = -741015642556489.0_wp/1473710148590233.0_wp aI(4,6) = -351847077835969.0_wp/518267159089510.0_wp aI(5,6) = 73303710171213.0_wp/949479256707403.0_wp aI(6,6) = 228857372167489.0_wp/1072948703211830.0_wp aI(7,6) = 785047896003256.0_wp/1277255591155965.0_wp aI(1,7) = 83804707700673.0_wp/388624687446694.0_wp aI(2,7) = 112077896806234.0_wp/1019114741691147.0_wp aI(3,7) = 303265399366288.0_wp/952204994665799.0_wp aI(4,7) = 15356355927452.0_wp/35907594911337.0_wp aI(5,7) = -27839028985592.0_wp/1162483488747029.0_wp aI(6,7) = -44139863014863.0_wp/867543818735444.0_wp aI(7,7) = -93564869305313.0_wp/374061922633495.0_wp ! ======= bE(1) = 342058879474588.0_wp/247719565460375.0_wp bE(2) = -1242156892003476.0_wp/821956816784831.0_wp bE(3) = 47996106307509.0_wp/613169560650038.0_wp bE(4) = -513370256818603.0_wp/1083398076347323.0_wp bE(5) = 461378680164967.0_wp/397240231852477.0_wp bE(6) = 785047896003256.0_wp/1277255591155965.0_wp bE(7) = -93564869305313.0_wp/374061922633495.0_wp ! ======= bEh(1) = 991417089953590.0_wp/999909103080897.0_wp bEh(2) = -532827012667917.0_wp/651724446129560.0_wp bEh(3) = 358809077318909.0_wp/997779313389769.0_wp bEh(4) = 750730560172731.0_wp/1275392967392356.0_wp bEh(5) = -223531138026967.0_wp/1489301836546267.0_wp bEh(6) = -1.0_wp/5.0_wp bEh(7) = 1728909943061667.0_wp/7585787459483518.0_wp ! ======= cE(1) = 315.0_wp/1478.0_wp cE(2) = 160.0_wp/563.0_wp cE(3) = 901.0_wp/2075.0_wp cE(4) = 312.0_wp/457.0_wp cE(5) = 220.0_wp/427.0_wp cE(6) = 1071.0_wp/1142.0_wp cE(7) = 1.0_wp/1.0_wp ! ======= g = 2041.0_wp/10000.0_wp ! ======= s(1,1) = 13884668392930.0_wp/234640369937491.0_wp s(2,1) = 10030900316005.0_wp/2086651180696992.0_wp s(3,1) = -118926908001586.0_wp/741556480234705.0_wp s(4,1) = 163389078737796.0_wp/1676938597354207.0_wp s(5,1) = -81409724936607.0_wp/858304079330089.0_wp s(6,1) = 319728859087345.0_wp/673977848232406.0_wp s(7,1) = 217.0_wp/500.0_wp s(1,2) = -111924915847013.0_wp/1243578048073566.0_wp s(2,2) = -62673149138093.0_wp/761465978621715.0_wp s(3,2) = -1457717872423556.0_wp/5505358634971407.0_wp s(4,2) = 771859583982829.0_wp/793560781909564.0_wp s(5,2) = 322889295503924.0_wp/899799578278057.0_wp s(6,2) = 690850749542290.0_wp/972787271713013.0_wp s(7,2) = -137.0_wp/1000.0_wp s(1,3) = 1199343886032593.0_wp/654921782933786.0_wp s(2,3) = 1182964664526971.0_wp/899335587864597.0_wp s(3,3) = -3684513303517213.0_wp/1388292422159759.0_wp s(4,3) = -5807497627726841.0_wp/3646133147584209.0_wp s(5,3) = -1148507005194423.0_wp/721499965982111.0_wp s(6,3) = 591543083950045.0_wp/574731519529754.0_wp s(7,3) = 19.0_wp/1000.0_wp s(1,4) = -6401941315505151.0_wp/515912413620623.0_wp s(2,4) = -11479209389157228.0_wp/1368511250198383.0_wp s(3,4) = 4071172898461189.0_wp/842352222047766.0_wp s(4,4) = 1411297603653727.0_wp/677061483401999.0_wp s(5,4) = 15852417762707122.0_wp/1975560909115597.0_wp s(6,4) = -9688805162168654.0_wp/1343665809655477.0_wp s(7,4) = -219.0_wp/500.0_wp s(1,5) = 28727638579444078.0_wp/813414156902871.0_wp s(2,5) = 78238937606712389.0_wp/1736600738523312.0_wp s(3,5) = 82092391266613375.0_wp/1403579858338522.0_wp s(4,5) = -23310318193897411.0_wp/1331440923797542.0_wp s(5,5) = 17943613659692992.0_wp/814401710950203.0_wp s(6,5) = 5133417605418287.0_wp/861982502393729.0_wp s(7,5) = 2047.0_wp/40.0_wp s(1,6) = 170374990866475687.0_wp/1132419499428970.0_wp s(2,6) = -92826333827584669.0_wp/795003401369665.0_wp s(3,6) = -6079510975043802383.0_wp/8798508153772343.0_wp s(4,6) = 64181179682972813.0_wp/2709856686863621.0_wp s(5,6) = -464159630914273131.0_wp/868997965155074.0_wp s(6,6) = 78767728338978230.0_wp/395150135553529.0_wp s(7,6) = -506647.0_wp/1000.0_wp s(1,7) = 2759804268534772681.0_wp/2553917080411984.0_wp s(2,7) = -871676801219517295.0_wp/518190491703074.0_wp s(3,7) = -7535154066810288087.0_wp/656055885585335.0_wp s(4,7) = -975868075615430859.0_wp/981717577311134.0_wp s(5,7) = -8631519879070296515.0_wp/1130568142313476.0_wp s(6,7) = 3100450007869423784.0_wp/1251320947580945.0_wp s(7,7) = -142287.0_wp/20.0_wp ! ======= sinv(1,1) = -224583810743497.0_wp/835658459684364.0_wp sinv(2,1) = -34272205822221.0_wp/928263910684753.0_wp sinv(3,1) = 1668832798627285.0_wp/1184318715197992.0_wp sinv(4,1) = 193932798991100.0_wp/960768572079533.0_wp sinv(5,1) = -4422333570519.0_wp/567830984102087.0_wp sinv(6,1) = 24436899127039.0_wp/1382845012238094.0_wp sinv(7,1) = -2105531783949.0_wp/1572654837832550.0_wp sinv(1,2) = -266340219889795.0_wp/194128712471624.0_wp sinv(2,2) = 451331801192905.0_wp/1910078891311353.0_wp sinv(3,2) = -1517438867816515.0_wp/1223893929609999.0_wp sinv(4,2) = -3191974337205863.0_wp/6839173715927833.0_wp sinv(5,2) = -38611815516196.0_wp/982293300916963.0_wp sinv(6,2) = -23925701496773.0_wp/1061307446938191.0_wp sinv(7,2) = 869275205439.0_wp/689974113077162.0_wp sinv(1,3) = 194083424557917.0_wp/596015596186465.0_wp sinv(2,3) = -59813143004998.0_wp/960228521504825.0_wp sinv(3,3) = -221106274845421.0_wp/391963754980713.0_wp sinv(4,3) = 174094560410129.0_wp/1226805748548574.0_wp sinv(5,3) = 69106153326872.0_wp/1177198877332049.0_wp sinv(6,3) = 2697357776123.0_wp/870195461216581.0_wp sinv(7,3) = 302800293331.0_wp/1425983567760854.0_wp sinv(1,4) = -151323120320761.0_wp/420802701537120.0_wp sinv(2,4) = -34887964106540.0_wp/134559320735893.0_wp sinv(3,4) = -508219926509968.0_wp/1412855673360475.0_wp sinv(4,4) = -804925454081409.0_wp/1688367508630018.0_wp sinv(5,4) = -15437501840549.0_wp/145453568799292.0_wp sinv(6,4) = -8128634146325.0_wp/855541573587084.0_wp sinv(7,4) = -90208029193.0_wp/1196846626638976.0_wp sinv(1,5) = -986431919640355.0_wp/1094629525967692.0_wp sinv(2,5) = 1648310699035691.0_wp/1416522406493986.0_wp sinv(3,5) = 270055782607000.0_wp/239102658130867.0_wp sinv(4,5) = 308741974894477.0_wp/837785740241172.0_wp sinv(5,5) = 71839747386566.0_wp/1568130372042529.0_wp sinv(6,5) = 20795725555026.0_wp/1926207924580201.0_wp sinv(7,5) = -1290469871861.0_wp/2405955585539766.0_wp sinv(1,6) = 997552819096673.0_wp/907177951296954.0_wp sinv(2,6) = 753567172972702.0_wp/741225315122187.0_wp sinv(3,6) = -232448852793691.0_wp/1062506123984403.0_wp sinv(4,6) = 39055111701635.0_wp/88703625360441.0_wp sinv(5,6) = 250931436067465.0_wp/2031620944171006.0_wp sinv(6,6) = 4350256034075.0_wp/584568766938861.0_wp sinv(7,6) = 382805575637.0_wp/1011913444644642.0_wp sinv(1,7) = 316685334255365.0_wp/273441938015053.0_wp sinv(2,7) = -547726721442317.0_wp/668487843817165.0_wp sinv(3,7) = 208172959453409.0_wp/1157249607735424.0_wp sinv(4,7) = -341607478795681.0_wp/1295894870517333.0_wp sinv(5,7) = -67245837211427.0_wp/862361284163790.0_wp sinv(6,7) = -18702670696353.0_wp/4016706188656877.0_wp sinv(7,7) = -225718789055.0_wp/846187954928258.0_wp ! ======= jcf(1,1) = 2041.0_wp/10000.0_wp jcf(2,1) = 0.0_wp/1.0_wp jcf(3,1) = 0.0_wp/1.0_wp jcf(4,1) = 0.0_wp/1.0_wp jcf(5,1) = 0.0_wp/1.0_wp jcf(6,1) = 0.0_wp/1.0_wp jcf(7,1) = 0.0_wp/1.0_wp jcf(1,2) = 1.0_wp/1.0_wp jcf(2,2) = 2041.0_wp/10000.0_wp jcf(3,2) = 0.0_wp/1.0_wp jcf(4,2) = 0.0_wp/1.0_wp jcf(5,2) = 0.0_wp/1.0_wp jcf(6,2) = 0.0_wp/1.0_wp jcf(7,2) = 0.0_wp/1.0_wp jcf(1,3) = 0.0_wp/1.0_wp jcf(2,3) = 1.0_wp/1.0_wp jcf(3,3) = 2041.0_wp/10000.0_wp jcf(4,3) = 0.0_wp/1.0_wp jcf(5,3) = 0.0_wp/1.0_wp jcf(6,3) = 0.0_wp/1.0_wp jcf(7,3) = 0.0_wp/1.0_wp jcf(1,4) = 0.0_wp/1.0_wp jcf(2,4) = 0.0_wp/1.0_wp jcf(3,4) = 1.0_wp/1.0_wp jcf(4,4) = 2041.0_wp/10000.0_wp jcf(5,4) = 0.0_wp/1.0_wp jcf(6,4) = 0.0_wp/1.0_wp jcf(7,4) = 0.0_wp/1.0_wp jcf(1,5) = 0.0_wp/1.0_wp jcf(2,5) = 0.0_wp/1.0_wp jcf(3,5) = 0.0_wp/1.0_wp jcf(4,5) = 1.0_wp/1.0_wp jcf(5,5) = 2041.0_wp/10000.0_wp jcf(6,5) = 0.0_wp/1.0_wp jcf(7,5) = 0.0_wp/1.0_wp jcf(1,6) = 0.0_wp/1.0_wp jcf(2,6) = 0.0_wp/1.0_wp jcf(3,6) = 0.0_wp/1.0_wp jcf(4,6) = 0.0_wp/1.0_wp jcf(5,6) = 1.0_wp/1.0_wp jcf(6,6) = 2041.0_wp/10000.0_wp jcf(7,6) = 0.0_wp/1.0_wp jcf(1,7) = 0.0_wp/1.0_wp jcf(2,7) = 0.0_wp/1.0_wp jcf(3,7) = 0.0_wp/1.0_wp jcf(4,7) = 0.0_wp/1.0_wp jcf(5,7) = 0.0_wp/1.0_wp jcf(6,7) = 1.0_wp/1.0_wp jcf(7,7) = 2041.0_wp/10000.0_wp ! ======= q(1,1) = -74173778003186.0_wp/851201897099829.0_wp q(1,2) = -161442752974919.0_wp/1372228782161028.0_wp q(1,3) = 588811710819229.0_wp/1429733279531747.0_wp q(1,4) = -474800425140695.0_wp/818344979923196.0_wp q(1,5) = 145622171562358.0_wp/1135737590055179.0_wp q(1,6) = -7254104644621.0_wp/842788727260764.0_wp q(1,7) = 954361711909219.0_wp/1413571149514804.0_wp q(2,1) = -6497095689585.0_wp/917791780616324.0_wp q(2,2) = -324788217499153.0_wp/4422448798635346.0_wp q(2,3) = 413208724118165.0_wp/1278019410394237.0_wp q(2,4) = -491213389965485.0_wp/1307258458110309.0_wp q(2,5) = 1017311321000757.0_wp/1974017135173955.0_wp q(2,6) = -261988062705647.0_wp/928531239224153.0_wp q(2,7) = -551951573627673.0_wp/868779434993566.0_wp q(3,1) = 435759042681284.0_wp/1845123647330127.0_wp q(3,2) = -40090987585129.0_wp/350198681824630.0_wp q(3,3) = -351732038840582.0_wp/524820331942975.0_wp q(3,4) = -3452259233801737.0_wp/5560415114143492.0_wp q(3,5) = -23601870903605.0_wp/1313680413993738.0_wp q(3,6) = 171538583253559.0_wp/589424581900771.0_wp q(3,7) = -67338926156191.0_wp/628865062563894.0_wp q(4,1) = -101954732278433.0_wp/710585735951213.0_wp q(4,2) = 644542846739388.0_wp/846894697029131.0_wp q(4,3) = -147808601864945.0_wp/847785603828173.0_wp q(4,4) = -21545003732369.0_wp/86485786849853.0_wp q(4,5) = -170463277554779.0_wp/847275894814603.0_wp q(4,6) = -613449696111293.0_wp/1189843172459221.0_wp q(4,7) = 32532052531628.0_wp/855929159266327.0_wp q(5,1) = 258221907768775.0_wp/1848727641548511.0_wp q(5,2) = 87636439958686.0_wp/235981840721183.0_wp q(5,3) = -343569955262871.0_wp/1564827531144430.0_wp q(5,4) = 167741348227875.0_wp/711204716523316.0_wp q(5,5) = 283955502617206.0_wp/356742719317177.0_wp q(5,6) = 169906268661721.0_wp/949482977156046.0_wp q(5,7) = 360364484256404.0_wp/1332339091199197.0_wp q(6,1) = -762082157259048.0_wp/1090888939158431.0_wp q(6,2) = 341649847192803.0_wp/1236037000265683.0_wp q(6,3) = 99711217406954.0_wp/939517105474451.0_wp q(6,4) = -60617900078028.0_wp/547717963654571.0_wp q(6,5) = -13333861963703.0_wp/774268701406449.0_wp q(6,6) = 525642698932173.0_wp/857944624585067.0_wp q(6,7) = -121197542488657.0_wp/635319194869354.0_wp q(7,1) = -450391957640419.0_wp/704718800067350.0_wp q(7,2) = -703377571416843.0_wp/1685631967348262.0_wp q(7,3) = -262529551485247.0_wp/607371712278048.0_wp q(7,4) = 223749340697995.0_wp/2719056680051122.0_wp q(7,5) = 115379268767451.0_wp/554393028947246.0_wp q(7,6) = -319396516450588.0_wp/792545204629257.0_wp q(7,7) = 140362222982231.0_wp/1043475884822326.0_wp ! ======= t(1,1) = 2041.0_wp/10000.0_wp t(1,2) = -354987662412033.0_wp/613677340227106.0_wp t(1,3) = -794905360908234.0_wp/2034864564909977.0_wp t(1,4) = -370968900444055.0_wp/795820872868964.0_wp t(1,5) = -415728041276675.0_wp/437235120639133.0_wp t(1,6) = -422766734376738.0_wp/391629122144561.0_wp t(1,7) = -1971736436481569.0_wp/907549586276435.0_wp t(2,1) = 0.0_wp/1.0_wp t(2,2) = 2041.0_wp/10000.0_wp t(2,3) = 329801813959259.0_wp/1035645072871735.0_wp t(2,4) = 423129320141057.0_wp/1409495646403855.0_wp t(2,5) = 423188213011404.0_wp/745391137697999.0_wp t(2,6) = -895474171701779.0_wp/1054812162549264.0_wp t(2,7) = 1040778288299717.0_wp/1871189336267854.0_wp t(3,1) = 0.0_wp/1.0_wp t(3,2) = 0.0_wp/1.0_wp t(3,3) = 2041.0_wp/10000.0_wp t(3,4) = 334525126426769.0_wp/860831074456571.0_wp t(3,5) = 147472145197341.0_wp/877737194743208.0_wp t(3,6) = -284188687836854.0_wp/1175119922863599.0_wp t(3,7) = -548117705086703.0_wp/559172391092150.0_wp t(4,1) = 0.0_wp/1.0_wp t(4,2) = 0.0_wp/1.0_wp t(4,3) = 0.0_wp/1.0_wp t(4,4) = 2041.0_wp/10000.0_wp t(4,5) = 157035215668981.0_wp/965163862739829.0_wp t(4,6) = 110221183712507.0_wp/170783166311616.0_wp t(4,7) = -2069271269244413.0_wp/987459624630215.0_wp t(5,1) = 0.0_wp/1.0_wp t(5,2) = 0.0_wp/1.0_wp t(5,3) = 0.0_wp/1.0_wp t(5,4) = 0.0_wp/1.0_wp t(5,5) = 2041.0_wp/10000.0_wp t(5,6) = 1095221105986178.0_wp/921862932646443.0_wp t(5,7) = 720883378319623.0_wp/270388168528247.0_wp t(6,1) = 0.0_wp/1.0_wp t(6,2) = 0.0_wp/1.0_wp t(6,3) = 0.0_wp/1.0_wp t(6,4) = 0.0_wp/1.0_wp t(6,5) = 0.0_wp/1.0_wp t(6,6) = 2041.0_wp/10000.0_wp t(6,7) = -70180812148470.0_wp/721153820238977.0_wp t(7,1) = 0.0_wp/1.0_wp t(7,2) = 0.0_wp/1.0_wp t(7,3) = 0.0_wp/1.0_wp t(7,4) = 0.0_wp/1.0_wp t(7,5) = 0.0_wp/1.0_wp t(7,6) = 0.0_wp/1.0_wp t(7,7) = 2041.0_wp/10000.0_wp !===================================================================================================================120 !===================================================================================================================120 ! ********************* SIRK6(5)8L[4]SA ********************* !===================================================================================================================120 !===================================================================================================================120 ! ! SIRK, 8-stage, order =6, stage-order = 4, ! Stiffly-accurate, internally L-stable on ALL stages ! ! D = 1.66724 ! Min{a,b} = {-1.34535, -1.34535} ! Max{a,b} = {1.66724, 1.66724} ! {Min.,Max} Eig(M), = {-2.7503, 2.76182} ! Cmeasure = 0.266146 ! {Min., Max., RMS} Eig(M)int = {-1.74034, -0.838911, 3.40194} ! Condition Number of S, {kappa(S)_{2,Inf}} = {321752., 548433.} ! c ! 17 89 99 201 323 521 197 ! c = {---, ---, ---, ---, ---, ---, ---, 1}, ! 112 421 272 355 415 567 200 ! ! g = 16/100 ! ! {A1,A2,A3,A4,A5,A6,A7} = {0, 0, 0, 0, 0, 0, 0.00031674022} ! Embedded method ! {A1,A2,A3,A4,A5,A6,A7} = {0, 0, 0, 0, 0, 0.00031745568, 0.00063503750} ! B,C,E = {2.0004, 2.9712, 0.99775} !============================================================== !===================================================================================================================120 casename='SIRK6[5]8L[4]SA ' ! SIRK6(5)8L[4]SA !===================================================================================================================120 ns = 8 aI(1,1) = 269570883029939665.0_wp/331674831632514566.0_wp aI(2,1) = 125772670721920401.0_wp/162124613931352459.0_wp aI(3,1) = 145489418645116010.0_wp/325050419411792461.0_wp aI(4,1) = 25958993343828703.0_wp/145908421991461677.0_wp aI(5,1) = 78548552968909917.0_wp/247607769560731381.0_wp aI(6,1) = 245210646202916096.0_wp/608599774113529763.0_wp aI(7,1) = 204279693383710993.0_wp/278377281019193493.0_wp aI(8,1) = 42844233904725781.0_wp/306608537187267181.0_wp aI(1,2) = -173322143057470473.0_wp/179576108495039885.0_wp aI(2,2) = -132455903994480199.0_wp/166019106936203911.0_wp aI(3,2) = -28930880033942773.0_wp/411999129751770637.0_wp aI(4,2) = 167749822601331812.0_wp/353051398750817281.0_wp aI(5,2) = 116993862909154743.0_wp/610268924991071812.0_wp aI(6,2) = 4031129601108493.0_wp/271848926804696600.0_wp aI(7,2) = -163250621434689603.0_wp/244108637768655476.0_wp aI(8,2) = 148523771785943774.0_wp/257794743174373335.0_wp aI(1,3) = 99072516173208544.0_wp/229185445114180855.0_wp aI(2,3) = 88296910359008141.0_wp/306214410359484152.0_wp aI(3,3) = -52422095821503152.0_wp/196440840846136329.0_wp aI(4,3) = -327998973207757798.0_wp/451195596516977579.0_wp aI(5,3) = -870967951174658289.0_wp/1924577658653388581.0_wp aI(6,3) = -34947361708837022.0_wp/128482296179088327.0_wp aI(7,3) = 165184564209613761.0_wp/379367093580901519.0_wp aI(8,3) = -694451210057151527.0_wp/771547093439640555.0_wp aI(1,4) = -41906622817382685.0_wp/248218958849173348.0_wp aI(2,4) = -4841864449348973.0_wp/224011777440909296.0_wp aI(3,4) = 171281518034106832.0_wp/301582460149749357.0_wp aI(4,4) = 350458907169523611.0_wp/289087168334277634.0_wp aI(5,4) = 712633044962863127.0_wp/670057157095801960.0_wp aI(6,4) = 414728180227585387.0_wp/462041881004981920.0_wp aI(7,4) = 46834154278272820.0_wp/223414421557675273.0_wp aI(8,4) = 817551006934380097.0_wp/523319762469009434.0_wp aI(1,5) = 27027357327935373.0_wp/604228893033957446.0_wp aI(2,5) = -67694824553608269.0_wp/524415933166540007.0_wp aI(3,5) = -363154579557993199.0_wp/509164709427898108.0_wp aI(4,5) = -1766454865067936273.0_wp/1487162097924792433.0_wp aI(5,5) = -1335396221658967827.0_wp/1594283336588292130.0_wp aI(6,5) = -340233730811266888.0_wp/527120452665821801.0_wp aI(7,5) = 20556731936445664.0_wp/262684672987882261.0_wp aI(8,5) = -108032879312695765.0_wp/80300679078296808.0_wp aI(1,6) = 4381286009657193.0_wp/275959614801729965.0_wp aI(2,6) = 77787484297820103.0_wp/293999474758558858.0_wp aI(3,6) = 378291433996723806.0_wp/449557450604062019.0_wp aI(4,6) = 3509467466787442895.0_wp/3275076884904867496.0_wp aI(5,6) = 248212107748603971.0_wp/249928418398614800.0_wp aI(6,6) = 189729413780828741.0_wp/174178764973180221.0_wp aI(7,6) = 152459421547044922.0_wp/533290129208452727.0_wp aI(8,6) = 743582462931690623.0_wp/445996296431698441.0_wp aI(1,7) = -19662097071745592.0_wp/327775905639499873.0_wp aI(2,7) = -138423315825207143.0_wp/311333436827460069.0_wp aI(3,7) = -349808294564763243.0_wp/393316213466493268.0_wp aI(4,7) = -232078632841350901.0_wp/508601156194794077.0_wp aI(5,7) = -163043833799419567.0_wp/184610729332786038.0_wp aI(6,7) = -67535674634968870.0_wp/55053627005495087.0_wp aI(7,7) = -100356199389490559.0_wp/419637584019074502.0_wp aI(8,7) = -399055158805306170.0_wp/396263628853972487.0_wp aI(1,8) = 6460523713804473.0_wp/160987086178877462.0_wp aI(2,8) = 41216995139588255.0_wp/149423520696383126.0_wp aI(3,8) = 89994730623645393.0_wp/201483518526225851.0_wp aI(4,8) = 51188293520736.0_wp/148806368065571975.0_wp aI(5,8) = 197523672438630791.0_wp/511662054305367633.0_wp aI(6,8) = 236063906693445793.0_wp/358520772900869707.0_wp aI(7,8) = 32581748939637822.0_wp/217360422955891985.0_wp aI(8,8) = 124915953380470529.0_wp/406722054475011836.0_wp !================================================================ bE(1) = 42844233904725781.0_wp/306608537187267181.0_wp bE(2) = 148523771785943774.0_wp/257794743174373335.0_wp bE(3) = -694451210057151527.0_wp/771547093439640555.0_wp bE(4) = 817551006934380097.0_wp/523319762469009434.0_wp bE(5) = -108032879312695765.0_wp/80300679078296808.0_wp bE(6) = 743582462931690623.0_wp/445996296431698441.0_wp bE(7) = -399055158805306170.0_wp/396263628853972487.0_wp bE(8) = 124915953380470529.0_wp/406722054475011836.0_wp !================================================================ bEh(1) = 74468595368519393.0_wp/257641559138640021.0_wp bEh(2) = 92645841224556447.0_wp/464219760140501777.0_wp bEh(3) = -57215570907920219.0_wp/174176478573724129.0_wp bEh(4) = 121498013809149781.0_wp/153663135633702134.0_wp bEh(5) = -208140412092392936.0_wp/457582338437486163.0_wp bEh(6) = 401896472833013005.0_wp/319415345717249896.0_wp bEh(7) = -1421379013638106027.0_wp/563176251137575190.0_wp bEh(8) = 420923732945085162.0_wp/237849283249781227.0_wp !================================================================ cE(1) = 17.0_wp/112.0_wp cE(2) = 89.0_wp/421.0_wp cE(3) = 99.0_wp/272.0_wp cE(4) = 201.0_wp/355.0_wp cE(5) = 323.0_wp/415.0_wp cE(6) = 521.0_wp/567.0_wp cE(7) = 197.0_wp/200.0_wp cE(8) = 1.0_wp/1.0_wp !================================================================ g = 4.0_wp/25.0_wp ! ======= s(1,1) = -3548212425365339.0_wp/144459620499423644.0_wp s(2,1) = 15647034169518927.0_wp/370424420296800511.0_wp s(3,1) = 33558038461726421.0_wp/302562775998636068.0_wp s(4,1) = -23881855481098385.0_wp/598357864539557228.0_wp s(5,1) = 17354123417226559.0_wp/244318361603075699.0_wp s(6,1) = 136280051405393941.0_wp/366718930912101223.0_wp s(7,1) = 130485945197536079.0_wp/287514010333468421.0_wp s(8,1) = 101.0_wp/200.0_wp s(1,2) = 86032132488932754.0_wp/535275672314464651.0_wp s(2,2) = 123693163762025126.0_wp/770891541512061191.0_wp s(3,2) = 6537971266866685.0_wp/296703295612952662.0_wp s(4,2) = 147236710102109035.0_wp/425123668979012946.0_wp s(5,2) = 513149735291268239.0_wp/348371818329323043.0_wp s(6,2) = 277133229520880429.0_wp/190981396460010564.0_wp s(7,2) = 166978342237884454.0_wp/255070138617545455.0_wp s(8,2) = 123.0_wp/200.0_wp s(1,3) = -109520610329179301.0_wp/59099519604282678.0_wp s(2,3) = 367549870310265911.0_wp/392276758411642475.0_wp s(3,3) = 1618505274891289712.0_wp/284508078545877519.0_wp s(4,3) = 23658908440486113.0_wp/34474991855383291.0_wp s(5,3) = -1262532586396829221.0_wp/408867878059755364.0_wp s(6,3) = -21890681450300165.0_wp/354796614330519276.0_wp s(7,3) = -72588471678614747.0_wp/789387769487745916.0_wp s(8,3) = 81.0_wp/50.0_wp s(1,4) = 4598518915674908404.0_wp/262011935582939705.0_wp s(2,4) = 4708882852838111837.0_wp/1053083781936548369.0_wp s(3,4) = -19759218705565863024.0_wp/756672563173177229.0_wp s(4,4) = -850498923789245131.0_wp/101692448635313884.0_wp s(5,4) = 930875488683736163.0_wp/48919027478370254.0_wp s(6,4) = 3084702531297099302.0_wp/384935762061542167.0_wp s(7,4) = 536520866619510117.0_wp/336411626468664911.0_wp s(8,4) = -1.0_wp/200.0_wp s(1,5) = -38701224521888732599.0_wp/337371463043162990.0_wp s(2,5) = -39171624925770559378.0_wp/392886235308725129.0_wp s(3,5) = 9680860675574505043.0_wp/227968429951768510.0_wp s(4,5) = 39793490503483141877.0_wp/348957106512645789.0_wp s(5,5) = -15330881243461044783.0_wp/304121832997860401.0_wp s(6,5) = -26381889125217306168.0_wp/279186153988442479.0_wp s(7,5) = -12015139092106178965.0_wp/469516593370880368.0_wp s(8,5) = -1703.0_wp/100.0_wp s(1,6) = 17377935891195852575.0_wp/30869388383338877.0_wp s(2,6) = 150536387660814419349.0_wp/200311315633112459.0_wp s(3,6) = 4370300225932286561.0_wp/13060877346037256.0_wp s(4,6) = -224536482822016257347.0_wp/358440530682514324.0_wp s(5,6) = -29479348594523216386.0_wp/237485092964738541.0_wp s(6,6) = 99550352463520936678.0_wp/198806368297481299.0_wp s(7,6) = 102111904135095722974.0_wp/373222592331408411.0_wp s(8,6) = 843.0_wp/5.0_wp s(1,7) = -1400649795725155794845.0_wp/332525066304956357.0_wp s(2,7) = 215251756508891803594.0_wp/143855055877022471.0_wp s(3,7) = 2693534846425384193943.0_wp/323180459147368667.0_wp s(4,7) = -1992309331614891976108.0_wp/290686439789247343.0_wp s(5,7) = -2092763166951659453265.0_wp/467488938623500351.0_wp s(6,7) = 1139459800785539973953.0_wp/202467627397058824.0_wp s(7,7) = -1448037879180572861008.0_wp/494706091573231671.0_wp s(8,7) = -1694.0_wp/1.0_wp s(1,8) = -6924033343897697894003.0_wp/358169720588708258.0_wp s(2,8) = 25879984804381404486984.0_wp/704484520193723039.0_wp s(3,8) = 9517811254060562682323.0_wp/143566072252483493.0_wp s(4,8) = -33534507193819736125767.0_wp/394768236630553358.0_wp s(5,8) = -10819120644335444557118.0_wp/322883782525067479.0_wp s(6,8) = 20302653605987432493368.0_wp/342331260349212683.0_wp s(7,8) = -6559286597805249245289.0_wp/223946420269894319.0_wp s(8,8) = -8380.0_wp/1.0_wp ! ======= sinv(1,1) = -200860359116646742.0_wp/253151403719124219.0_wp sinv(2,1) = -177544170830035866.0_wp/250061540449156427.0_wp sinv(3,1) = 176614650323608357.0_wp/294577645804075975.0_wp sinv(4,1) = -63002749603656385.0_wp/269179307095516178.0_wp sinv(5,1) = -33645045250803752.0_wp/293651196718497339.0_wp sinv(6,1) = -7550084425509130.0_wp/740846482785205427.0_wp sinv(7,1) = 315251764905337.0_wp/393891122162925696.0_wp sinv(8,1) = -46435091344567.0_wp/393967828665462058.0_wp sinv(1,2) = -21534371522721286.0_wp/40878009238123521.0_wp sinv(2,2) = 130673842086534785.0_wp/150406175276033226.0_wp sinv(3,2) = -86663528301270023.0_wp/337129950972018720.0_wp sinv(4,2) = 87702797562081707.0_wp/137766731079710901.0_wp sinv(5,2) = 46082518106197973.0_wp/216999563450625631.0_wp sinv(6,2) = 10293181064830599.0_wp/496590995687399558.0_wp sinv(7,2) = -182780660586829.0_wp/213753806187691791.0_wp sinv(8,2) = 58481137012982.0_wp/416956451347207347.0_wp sinv(1,3) = -340813158196771963.0_wp/429968836779579853.0_wp sinv(2,3) = 9333563423555816.0_wp/334570494098728901.0_wp sinv(3,3) = -138030532136962691.0_wp/1033291823128155258.0_wp sinv(4,3) = -134067160336648358.0_wp/163001619404682083.0_wp sinv(5,3) = -211013720654738766.0_wp/970278792878765305.0_wp sinv(6,3) = -3079882808141499.0_wp/150299368506672779.0_wp sinv(7,3) = 2731099381459.0_wp/17384732935477340.0_wp sinv(8,3) = -7670381992727.0_wp/104892302238012920.0_wp sinv(1,4) = -466274391299337739.0_wp/586611708738900470.0_wp sinv(2,4) = 135651401626200236.0_wp/399647473823787557.0_wp sinv(3,4) = 173733535235607929.0_wp/309256297288979530.0_wp sinv(4,4) = 93970261574050016.0_wp/106682594820325693.0_wp sinv(5,4) = 49475857770798011.0_wp/226495434900700289.0_wp sinv(6,4) = 7469084218993334.0_wp/352712595020635501.0_wp sinv(7,4) = 56273601077052.0_wp/306067609751989201.0_wp sinv(8,4) = 4029278877697.0_wp/134091920658620850.0_wp sinv(1,5) = -125377071567733689.0_wp/179141605210201013.0_wp sinv(2,5) = 187774967395179588.0_wp/317585522599006487.0_wp sinv(3,5) = -228141927691483541.0_wp/364433791940227311.0_wp sinv(4,5) = -296259940105713882.0_wp/300898413198554741.0_wp sinv(5,5) = -42817346592697351.0_wp/184373463703708950.0_wp sinv(6,5) = -8134174849074867.0_wp/358435006703156971.0_wp sinv(7,5) = -145599935652185.0_wp/327109345107565816.0_wp sinv(8,5) = -10448722680416.0_wp/753170479660575685.0_wp sinv(1,6) = 16991955661090457.0_wp/200629931896421053.0_wp sinv(2,6) = 27659955993050071.0_wp/406990928757037506.0_wp sinv(3,6) = 73018871834279556.0_wp/116459048085152629.0_wp sinv(4,6) = 384954869593398251.0_wp/407553997600632838.0_wp sinv(5,6) = 63586165442124949.0_wp/292407085658168100.0_wp sinv(6,6) = 16785341473944013.0_wp/797073337725233170.0_wp sinv(7,6) = 273939609980969.0_wp/523451086249023653.0_wp sinv(8,6) = 1443191580751.0_wp/215046594190585189.0_wp sinv(1,7) = 1012996129643521315.0_wp/1022434541085493437.0_wp sinv(2,7) = 114648215864364726.0_wp/528748993799675681.0_wp sinv(3,7) = -40982916722198137.0_wp/51355309993774269.0_wp sinv(4,7) = -140822717148057122.0_wp/328652816981866077.0_wp sinv(5,7) = -62691919327981859.0_wp/873689333012063158.0_wp sinv(6,7) = -895966545871636.0_wp/163138636722096437.0_wp sinv(7,7) = -1227945631406.0_wp/6373219857741103.0_wp sinv(8,7) = -1336215539874.0_wp/324079060655481685.0_wp sinv(1,8) = 410979473430836501.0_wp/330727167560904297.0_wp sinv(2,8) = -133939644187788713.0_wp/323101146235748098.0_wp sinv(3,8) = 266277536309943957.0_wp/568669066141387708.0_wp sinv(4,8) = 54508424591678656.0_wp/3861656302322232737.0_wp sinv(5,8) = -10885398289548737.0_wp/513968314662463798.0_wp sinv(6,8) = -884657174401061.0_wp/258347586798910835.0_wp sinv(7,8) = -9231173867583.0_wp/156806999436140663.0_wp sinv(8,8) = 604275803587.0_wp/357729379349860480.0_wp ! ======= jcf(1,1) = 4.0_wp/25.0_wp jcf(2,1) = 0.0_wp/1.0_wp jcf(3,1) = 0.0_wp/1.0_wp jcf(4,1) = 0.0_wp/1.0_wp jcf(5,1) = 0.0_wp/1.0_wp jcf(6,1) = 0.0_wp/1.0_wp jcf(7,1) = 0.0_wp/1.0_wp jcf(8,1) = 0.0_wp/1.0_wp jcf(1,2) = 1.0_wp/1.0_wp jcf(2,2) = 4.0_wp/25.0_wp jcf(3,2) = 0.0_wp/1.0_wp jcf(4,2) = 0.0_wp/1.0_wp jcf(5,2) = 0.0_wp/1.0_wp jcf(6,2) = 0.0_wp/1.0_wp jcf(7,2) = 0.0_wp/1.0_wp jcf(8,2) = 0.0_wp/1.0_wp jcf(1,3) = 0.0_wp/1.0_wp jcf(2,3) = 1.0_wp/1.0_wp jcf(3,3) = 4.0_wp/25.0_wp jcf(4,3) = 0.0_wp/1.0_wp jcf(5,3) = 0.0_wp/1.0_wp jcf(6,3) = 0.0_wp/1.0_wp jcf(7,3) = 0.0_wp/1.0_wp jcf(8,3) = 0.0_wp/1.0_wp jcf(1,4) = 0.0_wp/1.0_wp jcf(2,4) = 0.0_wp/1.0_wp jcf(3,4) = 1.0_wp/1.0_wp jcf(4,4) = 4.0_wp/25.0_wp jcf(5,4) = 0.0_wp/1.0_wp jcf(6,4) = 0.0_wp/1.0_wp jcf(7,4) = 0.0_wp/1.0_wp jcf(8,4) = 0.0_wp/1.0_wp jcf(1,5) = 0.0_wp/1.0_wp jcf(2,5) = 0.0_wp/1.0_wp jcf(3,5) = 0.0_wp/1.0_wp jcf(4,5) = 1.0_wp/1.0_wp jcf(5,5) = 4.0_wp/25.0_wp jcf(6,5) = 0.0_wp/1.0_wp jcf(7,5) = 0.0_wp/1.0_wp jcf(8,5) = 0.0_wp/1.0_wp jcf(1,6) = 0.0_wp/1.0_wp jcf(2,6) = 0.0_wp/1.0_wp jcf(3,6) = 0.0_wp/1.0_wp jcf(4,6) = 0.0_wp/1.0_wp jcf(5,6) = 1.0_wp/1.0_wp jcf(6,6) = 4.0_wp/25.0_wp jcf(7,6) = 0.0_wp/1.0_wp jcf(8,6) = 0.0_wp/1.0_wp jcf(1,7) = 0.0_wp/1.0_wp jcf(2,7) = 0.0_wp/1.0_wp jcf(3,7) = 0.0_wp/1.0_wp jcf(4,7) = 0.0_wp/1.0_wp jcf(5,7) = 0.0_wp/1.0_wp jcf(6,7) = 1.0_wp/1.0_wp jcf(7,7) = 4.0_wp/25.0_wp jcf(8,7) = 0.0_wp/1.0_wp jcf(1,8) = 0.0_wp/1.0_wp jcf(2,8) = 0.0_wp/1.0_wp jcf(3,8) = 0.0_wp/1.0_wp jcf(4,8) = 0.0_wp/1.0_wp jcf(5,8) = 0.0_wp/1.0_wp jcf(6,8) = 0.0_wp/1.0_wp jcf(7,8) = 1.0_wp/1.0_wp jcf(8,8) = 4.0_wp/25.0_wp ! ======= q(1,1) = -32869531059013.0_wp/1053648405591425.0_wp q(1,2) = -92957481848378.0_wp/735760691262899.0_wp q(1,3) = 197623607135423.0_wp/852651211052730.0_wp q(1,4) = -400036431682753.0_wp/677306836668827.0_wp q(1,5) = 62770944981298.0_wp/472533302643367.0_wp q(1,6) = 445974245785478.0_wp/1061993607879743.0_wp q(1,7) = -225544079297913.0_wp/1129442774806946.0_wp q(1,8) = 696056740595916.0_wp/1182258379726885.0_wp q(2,1) = 58942792612511.0_wp/1099211341938285.0_wp q(2,2) = -34583488419091.0_wp/758990929698531.0_wp q(2,3) = -151899626846607.0_wp/874069047121868.0_wp q(2,4) = -629074246686690.0_wp/1047201828452309.0_wp q(2,5) = -154219396808572.0_wp/2676539647999273.0_wp q(2,6) = 111477827006779.0_wp/366430199751952.0_wp q(2,7) = 137340738275287.0_wp/1046218047228398.0_wp q(2,8) = -645066396579240.0_wp/920699590860313.0_wp q(3,1) = 106561401630645.0_wp/756703972887508.0_wp q(3,2) = 191547908672553.0_wp/1587706255783445.0_wp q(3,3) = -1076770783841229.0_wp/1248652719344330.0_wp q(3,4) = -73886345166773.0_wp/1035716406289517.0_wp q(3,5) = -87654203759503.0_wp/650368945103063.0_wp q(3,6) = 29044217034160.0_wp/417100795088879.0_wp q(3,7) = 254425156967233.0_wp/1035375425766231.0_wp q(3,8) = 283379409722461.0_wp/775622404583926.0_wp q(4,1) = -133328802238441.0_wp/2629889461645255.0_wp q(4,2) = -678179264046237.0_wp/2645658158419121.0_wp q(4,3) = -336045383587038.0_wp/1167929599001603.0_wp q(4,4) = 258382803322063.0_wp/649737991322415.0_wp q(4,5) = 1303182644981397.0_wp/2485727603685598.0_wp q(4,6) = 858231091625023.0_wp/1698775408043329.0_wp q(4,7) = -304360947581437.0_wp/818879463435397.0_wp q(4,8) = -72176390566629.0_wp/480564345191939.0_wp q(5,1) = 56129431788556.0_wp/622993526608085.0_wp q(5,2) = -624163005581686.0_wp/779765496021231.0_wp q(5,3) = 70707786548491.0_wp/1121657620949998.0_wp q(5,4) = 24022430083644.0_wp/647677638967351.0_wp q(5,5) = 392054376947497.0_wp/3108589209453480.0_wp q(5,6) = -98863235154343.0_wp/1150171700963636.0_wp q(5,7) = 500333192082478.0_wp/887670048055327.0_wp q(5,8) = 95010016298042.0_wp/1368465647096129.0_wp q(6,1) = 495358898123509.0_wp/1050040816602430.0_wp q(6,2) = -412740029055565.0_wp/971107305700173.0_wp q(6,3) = -668250630975016.0_wp/5394026845492595.0_wp q(6,4) = -55926754716068.0_wp/799722661275149.0_wp q(6,5) = -158396339892264.0_wp/413497397703307.0_wp q(6,6) = -198882396839771.0_wp/816871893314940.0_wp q(6,7) = -311813847137717.0_wp/513020475386556.0_wp q(6,8) = -17184850392129.0_wp/510533565156134.0_wp q(7,1) = 964756717906950.0_wp/1674350832161713.0_wp q(7,2) = 304420551834160.0_wp/1989337725404581.0_wp q(7,3) = 252779675815367.0_wp/963670198844317.0_wp q(7,4) = 367694222688761.0_wp/1195056981703092.0_wp q(7,5) = -325280441438525.0_wp/984101771216868.0_wp q(7,6) = 798876061022906.0_wp/1418512218872081.0_wp q(7,7) = 230360592377734.0_wp/988969175350995.0_wp q(7,8) = 14790098541887.0_wp/716263386202895.0_wp q(8,1) = 595002472326163.0_wp/928017227767584.0_wp q(8,2) = 226008369221188.0_wp/947315361862929.0_wp q(8,3) = 5478272663312.0_wp/140367929793295.0_wp q(8,4) = -100515536593620.0_wp/621821591309249.0_wp q(8,5) = 746823110378507.0_wp/1160531333196531.0_wp q(8,6) = -245203182293974.0_wp/830463435545725.0_wp q(8,7) = 75205457669720.0_wp/1376970636717483.0_wp q(8,8) = -15471126938461.0_wp/1836063540620563.0_wp ! ======= t(1,1) = 180244350371637.0_wp/1126868276263618.0_wp t(1,2) = -392583468178750.0_wp/828881219713327.0_wp t(1,3) = -490045535918397.0_wp/875960756546638.0_wp t(1,4) = -190933022178950.0_wp/360901038824607.0_wp t(1,5) = 1130441123439817.0_wp/1001785426529180.0_wp t(1,6) = -411593994924900.0_wp/1294802177543183.0_wp t(1,7) = -6349752375614477.0_wp/2050000149117882.0_wp t(1,8) = -13022786495141.0_wp/107570762091310.0_wp t(2,1) = 0.0_wp/1.0_wp t(2,2) = 85288341566735.0_wp/533166259630668.0_wp t(2,3) = 364391849692265.0_wp/1281179727879002.0_wp t(2,4) = 282427519409327.0_wp/847509782376348.0_wp t(2,5) = -316253337224677.0_wp/404055296629515.0_wp t(2,6) = 305176606279235.0_wp/1895646984777073.0_wp t(2,7) = 1266878767846480.0_wp/681911013172681.0_wp t(2,8) = 422188642953562.0_wp/1664850210133027.0_wp t(3,1) = 0.0_wp/1.0_wp t(3,2) = -3090941.0_wp/749706123511361.0_wp t(3,3) = 85288341566735.0_wp/533166259630668.0_wp t(3,4) = 236328209620645.0_wp/561859287470453.0_wp t(3,5) = -410966791850897.0_wp/695378559556228.0_wp t(3,6) = 195652180864971.0_wp/704155521594584.0_wp t(3,7) = 1746091609096721.0_wp/964952745920769.0_wp t(3,8) = 705171343261765.0_wp/1301705535214028.0_wp t(4,1) = 0.0_wp/1.0_wp t(4,2) = 0.0_wp/1.0_wp t(4,3) = 0.0_wp/1.0_wp t(4,4) = 60860727377309.0_wp/380379557091291.0_wp t(4,5) = -200825814647765.0_wp/1039950773828948.0_wp t(4,6) = 634435057463647.0_wp/1562548340843445.0_wp t(4,7) = 36110898164319.0_wp/719029562510054.0_wp t(4,8) = -1312796603747621.0_wp/1015943947240410.0_wp t(5,1) = 0.0_wp/1.0_wp t(5,2) = 0.0_wp/1.0_wp t(5,3) = 0.0_wp/1.0_wp t(5,4) = 4145023.0_wp/341215461830388.0_wp t(5,5) = 60860727377309.0_wp/380379557091291.0_wp t(5,6) = 288457721365118.0_wp/663270527454401.0_wp t(5,7) = -1266905243847901.0_wp/618980828012415.0_wp t(5,8) = -754886232959789.0_wp/567349623221281.0_wp t(6,1) = 0.0_wp/1.0_wp t(6,2) = 0.0_wp/1.0_wp t(6,3) = 0.0_wp/1.0_wp t(6,4) = 0.0_wp/1.0_wp t(6,5) = 0.0_wp/1.0_wp t(6,6) = 250909322856947.0_wp/1567847668296140.0_wp t(6,7) = -441585561543613.0_wp/2895586895038540.0_wp t(6,8) = 2224206094287016.0_wp/1545385893645085.0_wp t(7,1) = 0.0_wp/1.0_wp t(7,2) = 0.0_wp/1.0_wp t(7,3) = 0.0_wp/1.0_wp t(7,4) = 0.0_wp/1.0_wp t(7,5) = 0.0_wp/1.0_wp t(7,6) = 11689046.0_wp/1519374183383503.0_wp t(7,7) = 250909322856947.0_wp/1567847668296140.0_wp t(7,8) = 256573320092538.0_wp/1181680499411275.0_wp t(8,1) = 0.0_wp/1.0_wp t(8,2) = 0.0_wp/1.0_wp t(8,3) = 0.0_wp/1.0_wp t(8,4) = 0.0_wp/1.0_wp t(8,5) = 0.0_wp/1.0_wp t(8,6) = 0.0_wp/1.0_wp t(8,7) = 0.0_wp/1.0_wp t(8,8) = 51762958647773.0_wp/323420578223002.0_wp !===================================================================================================================120 !===================================================================================================================120 ! ********************* SIRK5(4)7L[5]SA ********************* !===================================================================================================================120 !===================================================================================================================120 ! ! SIRK, 7-stage, order =5, stage-order = 5, ! Stiffly-accurate, internally L-stable on ALL stages ! ! D = 14.8025 ! Min{a,b} = {-14.8025, -12.7809} ! Max{a,b} = {13.0465, 9.59956} ! {Min.,Max} Eig(M), = {-5.63088, 675.442} ! Cmeasure = 0.3969 ! {Min., Max., RMS} Eig(M)int = {-6.34783, -5.60983, 14.6938} ! Condition Number of S, kappaI(S)_{2,Inf} = {494320., 797146.} ! ! 167 133 161 257 109 379 ! c = {---, ---, ---, ---, ---, ---, 1}, ! 382 365 264 359 169 405 ! ! g = 1/7 ! ! {A1,A2,A3,A4,A5,A6,A7} = {0,0,0,0,0, 0.00054118670, 0.00092860217} ! Embedded method ! {A1,A2,A3,A4,A5,A6,A7} = {0,0,0,0,0.00076382287, 0.0016218878, 0.0031579453} ! B,C,E = {2.12338, 2.83191, 0.708524}, !============================================================== !===================================================================================================================120 casename='SIRK5[4]7L[5]SA' ! SIRK5(4)7L[5]SA !===================================================================================================================120 ns = 7 aI(1,1) = -6959398125137693.0_wp/487354483412478.0_wp aI(2,1) = -14761751668478125.0_wp/997246396607286.0_wp aI(3,1) = -16054194764065017.0_wp/1090728268532242.0_wp aI(4,1) = -9114366213032318.0_wp/630706184716107.0_wp aI(5,1) = -3535651769386852.0_wp/268591704053503.0_wp aI(6,1) = -11996783419242664.0_wp/904468925812727.0_wp aI(7,1) = -8773125108496805.0_wp/686426532553586.0_wp aI(1,2) = 5248153179816419.0_wp/640354388479597.0_wp aI(2,2) = 7676275757941777.0_wp/916852583344133.0_wp aI(3,2) = 6893944587969082.0_wp/819808771350593.0_wp aI(4,2) = 6551929918118287.0_wp/789945314294067.0_wp aI(5,2) = 5277703510345904.0_wp/682152331119181.0_wp aI(6,2) = 5968515081802069.0_wp/766552517061710.0_wp aI(7,2) = 9659664075730697.0_wp/1274887517438308.0_wp aI(1,3) = 12592773310891114.0_wp/1048891760614213.0_wp aI(2,3) = 1472683394850107.0_wp/115853572424231.0_wp aI(3,3) = 12197847727566805.0_wp/934949525304538.0_wp aI(4,3) = 19428967217807226.0_wp/1546300075394543.0_wp aI(5,3) = 14250178485408243.0_wp/1351137920762893.0_wp aI(6,3) = 9989458692807408.0_wp/964849142077123.0_wp aI(7,3) = 12862698552790732.0_wp/1339926327792419.0_wp aI(1,4) = -17239768565917263.0_wp/1236287883631337.0_wp aI(2,4) = -9314566190072464.0_wp/631480020005347.0_wp aI(3,4) = -16435618374504583.0_wp/1111384836730986.0_wp aI(4,4) = -14795222865413813.0_wp/1029568148798487.0_wp aI(5,4) = -9493673717761561.0_wp/770491866435882.0_wp aI(6,4) = -28985901871493076.0_wp/2317577671088965.0_wp aI(7,4) = -12291736478370131.0_wp/1048191496206652.0_wp aI(1,5) = 2872655943827463.0_wp/472778874779599.0_wp aI(2,5) = 7871573132792188.0_wp/1256095924147217.0_wp aI(3,5) = 6225360940409198.0_wp/1024038485999581.0_wp aI(4,5) = 3355047403867687.0_wp/541837665305397.0_wp aI(5,5) = 6726199773407615.0_wp/1151234699644699.0_wp aI(6,5) = 5477117210031022.0_wp/856122179552349.0_wp aI(7,5) = 3776740118599985.0_wp/601705552983238.0_wp aI(1,6) = 9606772816923261.0_wp/2125278789546575.0_wp aI(2,6) = 4788711357540958.0_wp/978407155971915.0_wp aI(3,6) = 4786178353082867.0_wp/971469726773196.0_wp aI(4,6) = 4948178168743275.0_wp/1046329190210041.0_wp aI(5,6) = 2240240636528313.0_wp/599545298583188.0_wp aI(6,6) = 1649302584514662.0_wp/412003443196913.0_wp aI(7,6) = 4651784258075520.0_wp/1267955551167427.0_wp aI(1,7) = -660601838655360.0_wp/309280394740699.0_wp aI(2,7) = -2661810456580252.0_wp/1143469406199187.0_wp aI(3,7) = -1887139050575059.0_wp/804866923659600.0_wp aI(4,7) = -1734362828160869.0_wp/773308274999397.0_wp aI(5,7) = -2389925195772603.0_wp/1379396553122845.0_wp aI(6,7) = -1650162328224991.0_wp/899956439942291.0_wp aI(7,7) = -4734544907442629.0_wp/2932685053214474.0_wp ! ======= bE(1) = -8773125108496805.0_wp/686426532553586.0_wp bE(2) = 9659664075730697.0_wp/1274887517438308.0_wp bE(3) = 12862698552790732.0_wp/1339926327792419.0_wp bE(4) = -12291736478370131.0_wp/1048191496206652.0_wp bE(5) = 3776740118599985.0_wp/601705552983238.0_wp bE(6) = 4651784258075520.0_wp/1267955551167427.0_wp bE(7) = -4734544907442629.0_wp/2932685053214474.0_wp ! ======= bEh(1) = -17081550280930987.0_wp/1259587583764143.0_wp bEh(2) = 5946568925109313.0_wp/757415929220436.0_wp bEh(3) = 16723840936319911.0_wp/1447057440215881.0_wp bEh(4) = -13396131973658136.0_wp/976660006793063.0_wp bEh(5) = 6465814850763931.0_wp/1038507058979580.0_wp bEh(6) = 6457508643576915.0_wp/1295690406061672.0_wp bEh(7) = -1577759722556877.0_wp/674062325691920.0_wp ! ======= cE(1) = 167.0_wp/382.0_wp cE(2) = 133.0_wp/365.0_wp cE(3) = 161.0_wp/264.0_wp cE(4) = 257.0_wp/359.0_wp cE(5) = 109.0_wp/169.0_wp cE(6) = 379.0_wp/405.0_wp cE(7) = 1.0_wp/1.0_wp ! ======= g = 1.0_wp/7.0_wp ! ======= s(1,1) = 4144219520018.0_wp/1146912532528581.0_wp s(2,1) = 18738251410588.0_wp/3309002732892103.0_wp s(3,1) = -19503591937142.0_wp/1196193351630431.0_wp s(4,1) = -11612326206344.0_wp/854797736069977.0_wp s(5,1) = -4189453857279.0_wp/736399192698734.0_wp s(6,1) = 47246926880747.0_wp/1113328300205546.0_wp s(7,1) = 17.0_wp/250.0_wp s(1,2) = -26883486012219.0_wp/967768487393333.0_wp s(2,2) = -26152669933574.0_wp/809872078638311.0_wp s(3,2) = 50954114313727.0_wp/4001771778216874.0_wp s(4,2) = 219843405811570.0_wp/1903334098313361.0_wp s(5,2) = 91864283909078.0_wp/1015745330803123.0_wp s(6,2) = 349781502538029.0_wp/1086560269085483.0_wp s(7,2) = 159.0_wp/500.0_wp s(1,3) = 542710488948973.0_wp/1019154003270205.0_wp s(2,3) = 254994534818229.0_wp/589838964148669.0_wp s(3,3) = -1782790479597782.0_wp/6958648628024627.0_wp s(4,3) = -315203704765219.0_wp/696847542043691.0_wp s(5,3) = 334510202017655.0_wp/1512310831404273.0_wp s(6,3) = 45663327785982.0_wp/1870014504494437.0_wp s(7,3) = 27.0_wp/100.0_wp s(1,4) = -5902595656269147.0_wp/2213477941518368.0_wp s(2,4) = -1887549778528858.0_wp/1001552044777977.0_wp s(3,4) = -1774053568532425.0_wp/737488337447617.0_wp s(4,4) = -148700241994683.0_wp/144157468117301.0_wp s(5,4) = -2090266110262809.0_wp/1366950966308080.0_wp s(6,4) = 696799381506356.0_wp/2830620241719189.0_wp s(7,4) = -9.0_wp/100.0_wp s(1,5) = -430970898516728.0_wp/2491541393879603.0_wp s(2,5) = -6893538211485020.0_wp/686488139218311.0_wp s(3,5) = 39616069324780373.0_wp/1087751489245167.0_wp s(4,5) = 27043208945210421.0_wp/764464135276757.0_wp s(5,5) = 24234807636319331.0_wp/1054959135108096.0_wp s(6,5) = -2329226454686751.0_wp/1645874748133760.0_wp s(7,5) = -1.0_wp/1000.0_wp s(1,6) = 149133046072789231.0_wp/2533865462943342.0_wp s(2,6) = 15560762069947326.0_wp/1390690627732745.0_wp s(3,6) = 745047691382502817.0_wp/1257096951715110.0_wp s(4,6) = 112760059992317288.0_wp/188105678361331.0_wp s(5,6) = 228129081741930224.0_wp/800148228426541.0_wp s(6,6) = 27909766065488577.0_wp/510568889585876.0_wp s(7,6) = -9947.0_wp/1000.0_wp s(1,7) = 789181844449995947.0_wp/727669696792437.0_wp s(2,7) = 336201969402543202.0_wp/660512645280769.0_wp s(3,7) = 2676979939614743858.0_wp/461447422548071.0_wp s(4,7) = 4173337909675494657.0_wp/754934613740920.0_wp s(5,7) = 2247529268047174391.0_wp/810101560325704.0_wp s(6,7) = 430749539891059781.0_wp/1082940623877027.0_wp s(7,7) = -146501.0_wp/1000.0_wp ! ======= sinv(1,1) = -9847742459279645.0_wp/830016162627091.0_wp sinv(2,1) = 11149292578428830.0_wp/2384808110049461.0_wp sinv(3,1) = -25334850490644379.0_wp/988578913892985.0_wp sinv(4,1) = -3077919196999942.0_wp/146967371631279.0_wp sinv(5,1) = -114459613097347.0_wp/1303705526393454.0_wp sinv(6,1) = 618211357623167.0_wp/1037605157021918.0_wp sinv(7,1) = -72097969774742.0_wp/1027366478214531.0_wp sinv(1,2) = 5201367879625517.0_wp/430357485997235.0_wp sinv(2,2) = -2486214014133943.0_wp/478242516609424.0_wp sinv(3,2) = 23899448604393627.0_wp/1486206856119308.0_wp sinv(4,2) = 17362536984954383.0_wp/1466838233924803.0_wp sinv(5,2) = -7656651378889.0_wp/428794898116062.0_wp sinv(6,2) = -356877719108371.0_wp/1120344629024599.0_wp sinv(7,2) = 43138861785461.0_wp/1125782133349928.0_wp sinv(1,3) = 6400159911373648.0_wp/907513296176687.0_wp sinv(2,3) = 225641356210177.0_wp/1036087176597005.0_wp sinv(3,3) = 15414421143093957.0_wp/872515888791359.0_wp sinv(4,3) = 17271576214408906.0_wp/1012907212541233.0_wp sinv(5,3) = 364982202443473.0_wp/2584497278364937.0_wp sinv(6,3) = -472552322540961.0_wp/867123048172168.0_wp sinv(7,3) = 83903204533547.0_wp/1335378363633577.0_wp sinv(1,4) = 7429510084543013.0_wp/1328025663728323.0_wp sinv(2,4) = -1758255228071116.0_wp/878494012030867.0_wp sinv(3,4) = -25555707206445599.0_wp/1169802797915892.0_wp sinv(4,4) = -13395893879711742.0_wp/672271734558079.0_wp sinv(5,4) = -105691523300961.0_wp/628196683325521.0_wp sinv(6,4) = 1103355125501701.0_wp/1748991868442695.0_wp sinv(7,4) = -68802372896189.0_wp/947683845737802.0_wp sinv(1,5) = -12760646782001888.0_wp/764912768251283.0_wp sinv(2,5) = 1501166404684916.0_wp/1419675479237241.0_wp sinv(3,5) = 13920551551992361.0_wp/1088436992215049.0_wp sinv(4,5) = 5470533408177835.0_wp/604950888325636.0_wp sinv(5,5) = 71860116744972.0_wp/993710370450949.0_wp sinv(6,5) = -289018442753487.0_wp/1131089601235619.0_wp sinv(7,5) = 5985925055563.0_wp/200089980835096.0_wp sinv(1,6) = -48104948861953238.0_wp/1423290173020005.0_wp sinv(2,6) = 4709041470296325.0_wp/519774396358774.0_wp sinv(3,6) = 2574397737075577.0_wp/494727984867537.0_wp sinv(4,6) = 6691720528024903.0_wp/1098867308071298.0_wp sinv(5,6) = 16896861034141.0_wp/506358674601072.0_wp sinv(6,6) = -200778381787116.0_wp/930199228745443.0_wp sinv(7,6) = 10171992701706.0_wp/415491826537063.0_wp sinv(1,7) = 45883588254232199.0_wp/1245627230572259.0_wp sinv(2,7) = -11726812195800925.0_wp/2047027916979674.0_wp sinv(3,7) = -3020969816878953.0_wp/1323118054885591.0_wp sinv(4,7) = -462977907244461.0_wp/164816667524150.0_wp sinv(5,7) = -7777830285105.0_wp/928852906313534.0_wp sinv(6,7) = 247517357593699.0_wp/2390202368624611.0_wp sinv(7,7) = -11776536350129.0_wp/1008575161226489.0_wp ! ======= jcf(1,1) = 1.0_wp/7.0_wp jcf(2,1) = 0.0_wp/1.0_wp jcf(3,1) = 0.0_wp/1.0_wp jcf(4,1) = 0.0_wp/1.0_wp jcf(5,1) = 0.0_wp/1.0_wp jcf(6,1) = 0.0_wp/1.0_wp jcf(7,1) = 0.0_wp/1.0_wp jcf(1,2) = 1.0_wp/1.0_wp jcf(2,2) = 1.0_wp/7.0_wp jcf(3,2) = 0.0_wp/1.0_wp jcf(4,2) = 0.0_wp/1.0_wp jcf(5,2) = 0.0_wp/1.0_wp jcf(6,2) = 0.0_wp/1.0_wp jcf(7,2) = 0.0_wp/1.0_wp jcf(1,3) = 0.0_wp/1.0_wp jcf(2,3) = 1.0_wp/1.0_wp jcf(3,3) = 1.0_wp/7.0_wp jcf(4,3) = 0.0_wp/1.0_wp jcf(5,3) = 0.0_wp/1.0_wp jcf(6,3) = 0.0_wp/1.0_wp jcf(7,3) = 0.0_wp/1.0_wp jcf(1,4) = 0.0_wp/1.0_wp jcf(2,4) = 0.0_wp/1.0_wp jcf(3,4) = 1.0_wp/1.0_wp jcf(4,4) = 1.0_wp/7.0_wp jcf(5,4) = 0.0_wp/1.0_wp jcf(6,4) = 0.0_wp/1.0_wp jcf(7,4) = 0.0_wp/1.0_wp jcf(1,5) = 0.0_wp/1.0_wp jcf(2,5) = 0.0_wp/1.0_wp jcf(3,5) = 0.0_wp/1.0_wp jcf(4,5) = 1.0_wp/1.0_wp jcf(5,5) = 1.0_wp/7.0_wp jcf(6,5) = 0.0_wp/1.0_wp jcf(7,5) = 0.0_wp/1.0_wp jcf(1,6) = 0.0_wp/1.0_wp jcf(2,6) = 0.0_wp/1.0_wp jcf(3,6) = 0.0_wp/1.0_wp jcf(4,6) = 0.0_wp/1.0_wp jcf(5,6) = 1.0_wp/1.0_wp jcf(6,6) = 1.0_wp/7.0_wp jcf(7,6) = 0.0_wp/1.0_wp jcf(1,7) = 0.0_wp/1.0_wp jcf(2,7) = 0.0_wp/1.0_wp jcf(3,7) = 0.0_wp/1.0_wp jcf(4,7) = 0.0_wp/1.0_wp jcf(5,7) = 0.0_wp/1.0_wp jcf(6,7) = 1.0_wp/1.0_wp jcf(7,7) = 1.0_wp/7.0_wp ! ======= q(1,1) = 43850882924804.0_wp/1011921075324525.0_wp q(1,2) = -163268434073943.0_wp/994244427425342.0_wp q(1,3) = 894060855477621.0_wp/1433298789505151.0_wp q(1,4) = 207355533917114.0_wp/662999525806351.0_wp q(1,5) = -188066290188583.0_wp/2071024451165546.0_wp q(1,6) = 344088566391067.0_wp/788623963337034.0_wp q(1,7) = 835153045920250.0_wp/1562673512015149.0_wp q(2,1) = 125832027967880.0_wp/1852848937225563.0_wp q(2,2) = -677327881041947.0_wp/3133963840499948.0_wp q(2,3) = 1839094689167049.0_wp/4234159712092298.0_wp q(2,4) = 261756376242257.0_wp/944717730954432.0_wp q(2,5) = -323092677666281.0_wp/745292299237733.0_wp q(2,6) = -317810590586104.0_wp/496239987599911.0_wp q(2,7) = -199712246507403.0_wp/684368784972148.0_wp q(3,1) = -177482215458443.0_wp/907658284988712.0_wp q(3,2) = 210937414827209.0_wp/643096941441385.0_wp q(3,3) = -35875545872899.0_wp/877608838203605.0_wp q(3,4) = 614073656358057.0_wp/848235254635933.0_wp q(3,5) = 104076797451537.0_wp/889137360305792.0_wp q(3,6) = 216010230036421.0_wp/737622297636686.0_wp q(3,7) = -31178343241273.0_wp/65159635571308.0_wp q(4,1) = -104545029727013.0_wp/641694443864428.0_wp q(4,2) = 250368194024546.0_wp/380519740456337.0_wp q(4,3) = -38571841370485.0_wp/314432043646897.0_wp q(4,4) = 1103648111411547.0_wp/5511039446433511.0_wp q(4,5) = -60276988827497.0_wp/502259463420659.0_wp q(4,6) = -1052644643449776.0_wp/2589112898775089.0_wp q(4,7) = 805524584563205.0_wp/1456930000926396.0_wp q(5,1) = -38906832593785.0_wp/570246359115619.0_wp q(5,2) = 495143791527617.0_wp/1151977533497937.0_wp q(5,3) = 480338848148309.0_wp/761539643324904.0_wp q(5,4) = -368169854878082.0_wp/1007997878534855.0_wp q(5,5) = 548371418298147.0_wp/1173382404191162.0_wp q(5,6) = -801637802790089.0_wp/8432967123963377.0_wp q(5,7) = -123034232976181.0_wp/540032453022527.0_wp q(6,1) = 1292559557330983.0_wp/2539691695518473.0_wp q(6,2) = 440806785605275.0_wp/983153861404126.0_wp q(6,3) = 36872719567902.0_wp/880403537553125.0_wp q(6,4) = -253344123833133.0_wp/1147259638776344.0_wp q(6,5) = -153682819181721.0_wp/259320276852464.0_wp q(6,6) = 424505875111439.0_wp/1319814820927363.0_wp q(6,7) = -241280130490050.0_wp/1294129775929477.0_wp q(7,1) = 623968418781000.0_wp/765128622856123.0_wp q(7,2) = -9406843923025.0_wp/1337051995722091.0_wp q(7,3) = -102271576369107.0_wp/1328322478792838.0_wp q(7,4) = 121945922099837.0_wp/433734101947028.0_wp q(7,5) = 1121647886683343.0_wp/2470747877633610.0_wp q(7,6) = -226704989736469.0_wp/1196081685891634.0_wp q(7,7) = 66901181434653.0_wp/752357586074923.0_wp ! ======= t(1,1) = 1.0_wp/7.0_wp t(1,2) = 229378301654879.0_wp/750123997918710.0_wp t(1,3) = 631070149842565.0_wp/836325357194854.0_wp t(1,4) = -341632451358124.0_wp/304579979169663.0_wp t(1,5) = 523005498554017.0_wp/988823141162227.0_wp t(1,6) = -1852472618423584.0_wp/847658950997753.0_wp t(1,7) = -29919430411686859.0_wp/1361870033795279.0_wp t(2,1) = 0.0_wp/1.0_wp t(2,2) = 1.0_wp/7.0_wp t(2,3) = 123049411681103.0_wp/318426727549022.0_wp t(2,4) = -492891555788809.0_wp/1785710561512040.0_wp t(2,5) = 192009874771259.0_wp/887122996973415.0_wp t(2,6) = -1162063920902021.0_wp/660625863300281.0_wp t(2,7) = -34484033932588283.0_wp/937839606962312.0_wp t(3,1) = 0.0_wp/1.0_wp t(3,2) = 0.0_wp/1.0_wp t(3,3) = 1.0_wp/7.0_wp t(3,4) = -328910753022265.0_wp/1316929652337289.0_wp t(3,5) = 161459103626999.0_wp/1063107564588481.0_wp t(3,6) = -1384661272280719.0_wp/787422173166141.0_wp t(3,7) = -63567824581282015.0_wp/1692990742377161.0_wp t(4,1) = 0.0_wp/1.0_wp t(4,2) = 0.0_wp/1.0_wp t(4,3) = 0.0_wp/1.0_wp t(4,4) = 1.0_wp/7.0_wp t(4,5) = -270361706902496.0_wp/1527291664198867.0_wp t(4,6) = -198127980452945.0_wp/314606142238664.0_wp t(4,7) = -27642996557348524.0_wp/831869278312873.0_wp t(5,1) = 0.0_wp/1.0_wp t(5,2) = 0.0_wp/1.0_wp t(5,3) = 0.0_wp/1.0_wp t(5,4) = 0.0_wp/1.0_wp t(5,5) = 1.0_wp/7.0_wp t(5,6) = -188480681907382.0_wp/699978390761103.0_wp t(5,7) = 3553971565828551.0_wp/504851365405175.0_wp t(6,1) = 0.0_wp/1.0_wp t(6,2) = 0.0_wp/1.0_wp t(6,3) = 0.0_wp/1.0_wp t(6,4) = 0.0_wp/1.0_wp t(6,5) = 0.0_wp/1.0_wp t(6,6) = 1.0_wp/7.0_wp t(6,7) = 7930883229376013.0_wp/1018946034971274.0_wp t(7,1) = 0.0_wp/1.0_wp t(7,2) = 0.0_wp/1.0_wp t(7,3) = 0.0_wp/1.0_wp t(7,4) = 0.0_wp/1.0_wp t(7,5) = 0.0_wp/1.0_wp t(7,6) = 0.0_wp/1.0_wp t(7,7) = 1.0_wp/7.0_wp ! =======