Semi-Implicit Runge-Kutta Procedures with Error Estimates for the Numerical Integration of Stiff Systems of Ordinary Differential Equations
- 1 July 1976
- journal article
- Published by Association for Computing Machinery (ACM) in Journal of the ACM
- Vol. 23 (3) , 455-460
- https://doi.org/10.1145/321958.321966
Abstract
A -stable, semi-implicit Runge-Kutta procedures requiring at most one Jacobian evaluation per time step are developed for the approximate numerical integration of stiff systems of ordinary differential equations. A simple procedure for estimating the local truncation error is described and, with the help of this estimate, efficient integration procedures are derived. The algorithms are illustrated by direct application to a particular example.Keywords
This publication has 3 references indexed in Scilit:
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- Numerical solution of linear systems with widely separated time constantsProceedings of the IEEE, 1967
- Some general implicit processes for the numerical solution of differential equationsThe Computer Journal, 1963