Stability Criteria for Implicit Runge–Kutta Methods
- 1 February 1979
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Numerical Analysis
- Vol. 16 (1), 46-57
- https://doi.org/10.1137/0716004
Abstract
A comparison is made of two stability criteria. The first is a modification to nonautonomous problems of A-stability and the second is a similar modification of B-stability. It is shown that under certain mild conditions these two concepts are equivalent. A number of examples are given of methods that satisfy these new stability properties and it is also shown that the growth of errors can be estimated by an extension of this theory.Keywords
This publication has 3 references indexed in Scilit:
- Diagonally Implicit Runge–Kutta Methods for Stiff O.D.E.’sSIAM Journal on Numerical Analysis, 1977
- A stability property of implicit Runge-Kutta methodsBIT Numerical Mathematics, 1975
- A special stability problem for linear multistep methodsBIT Numerical Mathematics, 1963