Multigrid applied to singular perturbation problems
type: Item
instance of: scholarly article
title: Multigrid applied to singular perturbation problems
zbMATH Open document ID: 0639.65050
DOI: 10.1016/0096-3003(88)90112-9
author: David Kamowitz
published in: Applied Mathematics and Computation
publication date: 1988-01-01T00:00:00Z
full work available at URL: http://hdl.handle.net/2060/19870008011
review text: The solution of the singular perturbation problem (1) \(-\epsilon u''+b(x)u'=f\), \(u(0)=u_ 0\), \(u(1)=u_ 1\), \(1>>\epsilon >0\) via a multigrid algorithm is considered. Three model problems are studied: BL(b(x) does not change sign, problem BL exhibits a boundary layer at \(x=1)\), TP-1, TP-2 (b(x) changes sign, there are two boundary layers at \(x=0\), and \(x=1\), problems with turning point at \(x=0.5)\). A cursory review from the previous paper by the author and \textit{S. V. Parter} [ibid. 17, 153-184 (1985; Zbl 0608.65050)] on a multigrid algorithm used to solve (1) is given. Some results for convergence conclusions are repeated. Theoretical and experimental results for a number of different discretizations are presented. Many practical (from a computational point of view) but also theoretical questions are answered in comments on experimental results for BL, TP-1 and TP-2 problems.
reviewed by: Z.Schneider
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 34B05
Mathematics Subject Classification ID: 34E15
zbMATH DE Number: 4043177
zbMATH Keywords: numerical examples
zbMATH Keywords: singular perturbation problem
zbMATH Keywords: multigrid algorithm
zbMATH Keywords: boundary layer
zbMATH Keywords: turning point
zbMATH Keywords: convergence
describes a project that uses: LINPACK
MaRDI profile type: Publication
OpenAlex ID: W1966941897
cites work: Q3943082
cites work: Multi-Level Adaptive Solutions to Boundary-Value Problems
cites work: An Example of Ill-Conditioning in the Numerical Solution of Singular Perturbation Problems
cites work: A study of some multigrid ideas
cites work: Analysis of Some Difference Approximations for a Singular Perturbation Problem Without Turning Points
cites work: Remarks on Singular Perturbations with Turning Points
cites work: Multigrid Methods for Variational Problems
description: scientific article; zbMATH DE number 4043177