Linear and non-linear stability for general linear methods
type: Item
instance of: scholarly article
title: Linear and non-linear stability for general linear methods
zbMATH Open document ID: 0623.65074
published in: BIT
publication date: 1987-01-01T00:00:00Z
review text: Stability in a numerical method prevents the growth of the approximate solution of a differential equation for which the solution is bounded. A variety of concepts of stability have been developed. For one-leg methods, two extremes, namely A-stability and algebraic stability together with a spectrum between these extremes are equivalent. For Runge-Kutta methods, A-stability is distinguished from the others. In this paper it is shown that general linear methods distinguish more of these concepts. In particular, A-stability is weaker than weak AN- stability which is weaker than strong AN-stability, while Euclidean AN- stability is equivalent to algebraic stability for such methods. Sufficient conditions for the equivalence of strong AN-stability to algebraic stability are promised in a later paper.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 4011815
zbMATH Keywords: comparison of stability concepts
zbMATH Keywords: one-leg methods
zbMATH Keywords: A-stability
zbMATH Keywords: algebraic stability
zbMATH Keywords: Runge-Kutta methods
zbMATH Keywords: linear methods
zbMATH Keywords: AN-stability
zbMATH Keywords: strong AN- stability
author: J. C. Butcher
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4011815