Optimum Runge-Kutta methods-Reference-Cited by-同舟云学术

Optimum Runge-Kutta methods

Published:1964 Issue:86 Volume:18 Page:306-310
ISSN:0025-5718
Container-title:Mathematics of Computation
language:en
Short-container-title:Math. Comp.

Author:

Hull T. E.,Johnston R. L.

Abstract

The optimum Runge-Kutta method of a particular order is the one whose truncation error is a minimum. Various measures of the size of the truncation error are considered. The optimum method is practically independent of the measure being used. Moreover, among methods of the same order which one might consider using the difference in size of the estimated error is not more than a factor of 2 or 3. These results are confirmed in practice insofar as the choice of optimum method is concerned, but they underestimate the variation in error between different methods.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Link

http://www.ams.org/mcom/1964-18-086/S0025-5718-1964-0165700-6/S0025-5718-1964-0165700-6.pdf

Reference6 articles.

1. A process for the step-by-step integration of differential equations in an automatic digital computing machine;Gill, S.;Proc. Cambridge Philos. Soc.,1951

2. R. L. Johnston, “On optimum Runge-Kutta methods for the numerical solution of ordinary differential equations,” M.A. Thesis, University of British Columbia, 1961.

3. Deux formules optimales du type de Runge-Kutta;Kuntzmann, J.;Chiffres,1959

4. On the accuracy of Runge-Kutta’s method;Lotkin, Max;Math. Tables Aids Comput.,1951

5. Runge-Kutta methods with minimum error bounds;Ralston, Anthony;Math. Comp.,1962

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