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The uniform asymptotic swallowtail approximation - Practical methods for oscillating integrals with four coalescing saddle pointsMethods that can be used in the numerical implementation of the uniform swallowtail approximation are described. An explicit expression for that approximation is presented to the lowest order, showing that there are three problems which must be overcome in practice before the approximation can be applied to any given problem. It is shown that a recently developed quadrature method can be used for the accurate numerical evaluation of the swallowtail canonical integral and its partial derivatives. Isometric plots of these are presented to illustrate some of their properties. The problem of obtaining the arguments of the swallowtail integral from an analytical function of its argument is considered, describing two methods of solving this problem. The asymptotic evaluation of the butterfly canonical integral is addressed.
Document ID
19840040799
Acquisition Source
Legacy CDMS
Document Type
Reprint (Version printed in journal)
Authors
Connor, J. N. L.
(Manchester Univ. United Kingdom)
Curtis, P. R.
(Manchester, Victoria University Manchester, United Kingdom)
Farrelly, D.
(Colorado, University Boulder, CO, United States)
Date Acquired
August 12, 2013
Publication Date
February 1, 1984
Publication Information
Publication: Journal of Physics A - Mathematical and General
Volume: 17
ISSN: 0305-4470
Subject Category
Numerical Analysis
Accession Number
84A23586
Funding Number(s)
CONTRACT_GRANT: E(11-1)-3070
CONTRACT_GRANT: NSF CHE-80-11412
CONTRACT_GRANT: NSG-1323
CONTRACT_GRANT: NSF PHY-82-00805
Distribution Limits
Public
Copyright
Other

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