Towards Efficient Runge–Kutta Methods for Stiff Systems
Author:
- J. C. ButcherJBJ. C. Butcher
- 1 June 1990
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Numerical Analysis
- Vol. 27 (3) , 753-761
Abstract
A special class of implicit Runge–Kutta methods is developed for the numerical solution of stiff initial value problems. These formulae are derived from known singly implicit methods by adding one or more extra diagonally implicit stages. It is hoped that this modification of the original method will lead to an overall gain in efficiency, and an analysis of the advantages of making this enhancement is presented.Keywords
This publication has 9 references indexed in Scilit:
- Block Runge-Kutta methods for the numerical integration of initial value problems in ordinary differential equations. I. The nonstiff caseMathematics of Computation, 1983
- Block Runge-Kutta methods for the numerical integration of initial value problems in ordinary differential equations. II. The stiff caseMathematics of Computation, 1983
- The Concept of B-ConvergenceSIAM Journal on Numerical Analysis, 1981
- An implementation of singly-implicit Runge-Kutta methodsBIT Numerical Mathematics, 1980
- A Transformed implicit Runge-Kutta MethodJournal of the ACM, 1979
- A special family of Runge-Kutta methods for solving stiff differential equationsBIT Numerical Mathematics, 1978
- Diagonally Implicit Runge–Kutta Methods for Stiff O.D.E.’sSIAM Journal on Numerical Analysis, 1977
- Runge-Kutta methods with a multiple real eigenvalue onlyBIT Numerical Mathematics, 1976
- C-Polynomials for rational approximation to the exponential functionNumerische Mathematik, 1975