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Classical seventh-, sixth-, and fifth-order Runge-Kutta-Nystrom formulas with stepsize control for general second-order differential equationsRunge-Kutta-Nystrom formulas of the seventh, sixth, and fifth order were derived for the general second order (vector) differential equation written as the second derivative of x = f(t, x, the first derivative of x). The formulas include a stepsize control procedure, based on a complete coverage of the leading term of the local truncation error in x, and they require no more evaluations per step than the earlier Runge-Kutta formulas for the first derivative of x = f(t, x). The developed formulas are expected to be time saving in comparison to the Runge-Kutta formulas for first-order differential equations, since it is not necessary to convert the second-order differential equations into twice as many first-order differential equations. The examples shown saved from 25 percent to 60 percent more computer time than the earlier formulas for first-order differential equations, and are comparable in accuracy.
Document ID
19740026877
Document Type
Other - NASA Technical Report (TR)
Authors
Fehlberg, E. (NASA Marshall Space Flight Center Huntsville, AL, United States)
Date Acquired
September 3, 2013
Publication Date
October 1, 1974
Subject Category
MATHEMATICS
Report/Patent Number
NASA-TR-R-432
M-546
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

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