Mesh selection for stiff two-point boundary value problems
type: Item
instance of: scholarly article
title: Mesh selection for stiff two-point boundary value problems
zbMATH Open document ID: 0804.65077
DOI: 10.1007/BF02140684
published in: Numerical Algorithms
publication date: 1995-01-15T00:00:00Z
review text: The general structure of COLSYS is reviewed, in particular, some theoretical properties of collocation at Gaussian points are stated and it is demonstrated how these properties lead to the derivation of the algorithms for error estimation and mesh selection. The issue of error estimation for both stiff and non-stiff problems is considered, and special mention is made of an approach to stiff problems in which an error estimate is formed by using the solution at collocation points only. Also, it is demonstrated that the mesh selection algorithm of COLSYS is, in a sense, unstable when dealing with a rapidly varying monitor function. Modifications to the algorithm are suggested, and the question of how to estimate the error best with respect to these modifications is considered. The modifications to both the mesh selection and error estimation algorithms are incorporated into the latest version of COLSYS and tested on a set of linear singular perturbation problems within a continuation framework.
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 65L60
Mathematics Subject Classification ID: 65L50
Mathematics Subject Classification ID: 34E13
Mathematics Subject Classification ID: 34B05
zbMATH DE Number: 640743
zbMATH Keywords: stiff problems
zbMATH Keywords: COLSYS
zbMATH Keywords: collocation
zbMATH Keywords: algorithms
zbMATH Keywords: error estimation
zbMATH Keywords: mesh selection
zbMATH Keywords: non-stiff problems
zbMATH Keywords: singular perturbation
author: R. W. Wright
author: Jeff R. Cash
author: Gerald Moore
reviewed by: Pavol Chocholatý
describes a project that uses: AUTO
describes a project that uses: COLNEW
describes a project that uses: AUTO-86
describes a project that uses: COLSYS
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 640743