On the convergence of multistep methods for nonlinear stiff differential equations
type: Item
instance of: scholarly article
title: On the convergence of multistep methods for nonlinear stiff differential equations
zbMATH Open document ID: 0729.65055
DOI: 10.1007/BF01385657
published in: Numerische Mathematik
publication date: 1991-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/133533
review text: This work concerns an application of the general linear multistep methods of the form \(\sum^{k}_{j=0}\alpha_ jy_{n+j}=h\sum^{k}_{j=0}\beta_ jf_{n+j}\) to numerical integration of nonlinear stiff problems. A nice general definition of stiffness and an elegant analysis of convergence of so called A(\(\alpha\))-stable algorithms of the discussed form create a basis for further applications. This general framework is applied to: a) Singularly perturbed first order systems of the form \(u'=a(u,v),\epsilon v=b(u,v),\) \(0<\epsilon \ll 1.\) b) Nonlinear parabolic problems. In my opinion this nice work marks a step forward in the theory of multistep methods for nonlinear stiff problems.
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 34E13
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 65L70
zbMATH DE Number: 4205897
zbMATH Keywords: A-alpha-stability
zbMATH Keywords: linear multistep methods
zbMATH Keywords: nonlinear stiff problems
zbMATH Keywords: convergence
zbMATH Keywords: first order systems
author: Christian Lubich
MaRDI profile type: Publication
cites work: G-stability is equivalent toA-stability
cites work: On the uniform power-boundedness of a family of matrices and the applications to one-leg and linear multistep methods
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OpenAlex ID: W4234178278
description: scientific article; zbMATH DE number 4205897