Pseudo-Runge-Kutta Methods of the Fifth Order
- 1 October 1970
- journal article
- Published by Association for Computing Machinery (ACM) in Journal of the ACM
- Vol. 17 (4) , 613-628
- https://doi.org/10.1145/321607.321611
Abstract
A family of fifth-order pseudo-Runge-Kutta methods for the numerical solution of systems of ordinary differential equations is presented. A procedure for determining an “optimal” set of parameters is given, and several examples are considered. The principal advantage of these methods is that, for a fixed stepsize, they require two less function evaluations at each step than do the corresponding fifth-order Runge-Kutta methods. Their principal disadvantage is that they are not self-starting; they require two initial values. Numerically, pseudo-Runge-Kutta and Runge-Kutta methods seem to be comparable.Keywords
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