Some Practical Runge-Kutta Formulas
Open Access
- 1 January 1986
- journal article
- Published by JSTOR in Mathematics of Computation
- Vol. 46 (173) , 135-150
- https://doi.org/10.2307/2008219
Abstract
A new selection is made of the most practical of the many explicit Runge-Kutta formulas of order 4 which have been proposed. A new formula is considered, formulas are modified to improve their quality and efficiency in agreement with improved understanding of the issues, and formulas are derived which permit interpolation. It is possible to do a lot better than the pair of Fehlberg currently regarded as "best".Keywords
This publication has 12 references indexed in Scilit:
- A family of embedded Runge-Kutta formulaePublished by Elsevier ,2006
- Interpolation for Runge–Kutta MethodsSIAM Journal on Numerical Analysis, 1985
- Local error estimation by doublingComputing, 1985
- The step sizes used by one-step codes for ODEsApplied Numerical Mathematics, 1985
- Fourth- and Fifth-Order, Scaled Rungs–Kutta Algorithms for Treating Dense OutputSIAM Journal on Numerical Analysis, 1983
- Test Results on Initial Value Methods for Non-Stiff Ordinary Differential EquationsSIAM Journal on Numerical Analysis, 1976
- Local Extrapolation in the Solution of Ordinary Differential EquationsMathematics of Computation, 1973
- Comparing Numerical Methods for Ordinary Differential EquationsSIAM Journal on Numerical Analysis, 1972
- Comparing Error Estimators for Runge-Kutta MethodsMathematics of Computation, 1971
- Klassische Runge-Kutta-Formeln vierter und niedrigerer Ordnung mit Schrittweiten-Kontrolle und ihre Anwendung auf WärmeleitungsproblemeComputing, 1970