\(A_ 0\)-contractivity of the variable-step BDF's of order less than four
type: Item
instance of: scholarly article
title: \(A_ 0\)-contractivity of the variable-step BDF's of order less than four
zbMATH Open document ID: 0573.65069
DOI: 10.1007/BF01934383
author: Jørgen Sand
published in: BIT
publication date: 1985-01-01T00:00:00Z
review text: The author investigates the stability of the variable-step, variable- order backward differentiation formulas (BDF's), when applied to stiff differential equations. For \(y'=\lambda (t,y)y\) with real non-positive \(\lambda\) (t,y) it is shown that the numerical solution remains bounded for arbitrarily large stepsizes, provided that the stepsize-ratios satisfy some (very strong) restrictions. These restrictions were derived by a formula manipulation system.
reviewed by: Ernst Hairer
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 65L05
zbMATH DE Number: 3915556
zbMATH Keywords: contractivity
zbMATH Keywords: variable-step, variable-order backward differentiation formulas
zbMATH Keywords: stiff differential equations
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf01934383
OpenAlex ID: W1980906683
description: scientific article; zbMATH DE number 3915556