Time discretisation of parabolic problems with the variable 3-step BDF
type: Item
instance of: scholarly article
title: Time discretisation of parabolic problems with the variable 3-step BDF
zbMATH Open document ID: 1014.65086
DOI: 10.1023/A:1021992101967
published in: BIT
publication date: 2003-06-25T00:00:00Z
review text: The authors consider the stability of 3-step backward differentiation formula (BDF) on variable grids for the numerical integration of time-dependent parabolic equations. A stability inequality with a stability constant depending in a controllable way on the mesh is obtained. In particular if the ratios \(r_j\) of adjacent mesh-sizes of the underling grid satisfy the bound \(r_j \leq \bar r < 1.199\) than any mixture of the \(j\)-step BDF for \(j=1,2,3\) is stable. From the stability inequality error estimates can be obtained.
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 35K15
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65M50
Mathematics Subject Classification ID: 65M15
zbMATH DE Number: 1876907
zbMATH Keywords: parabolic equation
zbMATH Keywords: BDF method
zbMATH Keywords: variable step-size, variable order
zbMATH Keywords: stability
zbMATH Keywords: error estimate
zbMATH Keywords: backward differentiation formula
author: Manuel Calvo
author: Rolf Dieter Grigorieff
reviewed by: Qin Meng Zhao
MaRDI profile type: Publication
full work available at URL: a:1021992101967
OpenAlex ID: W51568807
description: scientific article; zbMATH DE number 1876907