Logarithmic norms and nonlinear DAE stability
type: Item
instance of: scholarly article
title: Logarithmic norms and nonlinear DAE stability
zbMATH Open document ID: 1019.65062
DOI: 10.1023/A:1021956621531
author: Gustaf Söderlind
author: Inmaculada Higueras
published in: BIT
publication date: 2003-03-24T00:00:00Z
review text: The authors discuss the use of logarithmic norms for the stability analysis of nonlinear differential algebraic equations (DAEs). The main idea is to introduce (restricted) least upper bound logarithmic Lipschitz constants defined with respect to the left and right semi-inner products in a Banach space. The definition is made in such a way that it also covers unbounded operators with a view towards the application to problems in partial differential equations. The case of nonlinear index 1 differential algebraic equations is studied in detail including an analysis of the discretised equations for some simple discretisations. For Runge-Kutta methods the relation to B-stability is studied.
reviewed by: Werner M. Seiler
Mathematics Subject Classification ID: 65L80
Mathematics Subject Classification ID: 34A09
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 65L06
zbMATH DE Number: 1876914
zbMATH Keywords: differential algebraic equation
zbMATH Keywords: logarithmic norm
zbMATH Keywords: logarithmic Lipschitz constant
zbMATH Keywords: nonlinear stability
zbMATH Keywords: error bounds
zbMATH Keywords: Runge-Kutta methods
MaRDI profile type: Publication
full work available at URL: a:1021956621531
OpenAlex ID: W1776430052
description: scientific article; zbMATH DE number 1876914