Stability Properties for a General Class of Methods for Ordinary Differential Equations
- 1 February 1981
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Numerical Analysis
- Vol. 18 (1) , 37-44
- https://doi.org/10.1137/0718004
Abstract
The concepts of G-stability for linear multistep methods and B-stability for Runge-Kutta methods are combined in a unified approach to nonlinear stability for a class of methods general enough to include these as special cases. Recent work on these developments, by Kevin Burrage and the author, is reviewed and, to exemplify the new ideas and techniques, an algebraic stability analysis is presented for the backward differentiation methods of orders 1, 2 and 3.Keywords
This publication has 4 references indexed in Scilit:
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- Stability Criteria for Implicit Runge–Kutta MethodsSIAM Journal on Numerical Analysis, 1979
- A stability property of implicit Runge-Kutta methodsBIT Numerical Mathematics, 1975
- On the convergence of numerical solutions to ordinary differential equationsMathematics of Computation, 1966