Error bounds for spatial discretization and waveform relaxation applied to parabolic functional differential equations
type: Item
instance of: scholarly article
title: Error bounds for spatial discretization and waveform relaxation applied to parabolic functional differential equations
zbMATH Open document ID: 1053.65078
author: B. Zubik-Kowal
published in: Journal of Mathematical Analysis and Applications
publication date: 2004-08-06T00:00:00Z
review text: The processes of semi-discretization and waveform relaxation are applied to general nonlinear parabolic functional differential equations. Two new theorems are presented, which extend and improve some of the classical results. The first of these theorems gives an upper bound for the norm of the error of finite difference semi-discretization. This upper bound is sharper than the classical error bound. The second of these theorems gives an upper bound for the norm of the error, which is caused by both semi-discretization and waveform relaxation. The focus in the paper is on estimating this error directly without using the upper bound for the error, which is caused by the process of semi-discretization and the upper bound for the error, which is caused by the waveform relaxation method. Such estimating gives sharper error bound than the bound, which is obtained by estimating both errors separately.
Mathematics Subject Classification ID: 65M15
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65M20
Mathematics Subject Classification ID: 35R10
Mathematics Subject Classification ID: 35K55
zbMATH DE Number: 2082158
zbMATH Keywords: partial functional differential equations
zbMATH Keywords: semi-discretization
zbMATH Keywords: waveform relaxation
zbMATH Keywords: error estimates
zbMATH Keywords: finite difference
reviewed by: Vit Dolejsi
MaRDI profile type: Publication
full work available at URL: j.jmaa.2004.01.012
OpenAlex ID: W2075116650
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DOI: 10.1016/J.JMAA.2004.01.012
description: scientific article; zbMATH DE number 2082158