On error structures and extrapolation for stiff systems, with application in the method of lines
type: Item
instance of: scholarly article
title: On error structures and extrapolation for stiff systems, with application in the method of lines
zbMATH Open document ID: 0716.65061
DOI: 10.1007/BF02241272
author: W. Auzinger
published in: Computing
publication date: 1990-01-01T00:00:00Z
review text: In this paper, which carries on the considerations in the author's earlier paper [ibid. 43, No.2, 115-131 (1989; Zbl 0685.65062)], the structure of the global error is studied for some time discretization schemes, applied to a class of stiff initial value problems as they typically arise from the semi-discretization of parabolic initial/boundary value problems (method of lines). The implicit Euler and trapezoidal schemes and a locally one-dimensional splitting method are considered, and `perturbed' asymptotic error expansions are derived which are valid independent of the stiffness (independent of the meshwidth in space). The key point within the analysis is a careful, quantitative description of the remainder term in such an expansion. The results are applicable in the method of lines setting and enable the prediction of the behavior of extrapolation algorithms for the class of problems under consideration. These theoretical considerations are illustrated by numerical examples.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65M20
Mathematics Subject Classification ID: 65L70
Mathematics Subject Classification ID: 34A30
Mathematics Subject Classification ID: 35G10
Mathematics Subject Classification ID: 35K25
Mathematics Subject Classification ID: 34E13
zbMATH DE Number: 4180687
zbMATH Keywords: stiff systems
zbMATH Keywords: error structures
zbMATH Keywords: global error
zbMATH Keywords: time discretization schemes
zbMATH Keywords: stiff initial value problems
zbMATH Keywords: semi-discretization
zbMATH Keywords: method of lines
zbMATH Keywords: implicit Euler and trapezoidal schemes
zbMATH Keywords: splitting method
zbMATH Keywords: asymptotic error expansions
zbMATH Keywords: extrapolation algorithms
zbMATH Keywords: numerical examples
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02241272
OpenAlex ID: W24638907
description: scientific article; zbMATH DE number 4180687