A polynomial based iterative method for linear parabolic equations
type: Item
instance of: scholarly article
title: A polynomial based iterative method for linear parabolic equations
zbMATH Open document ID: 0686.65083
DOI: 10.1016/0377-0427(90)90193-4
author: Mark J. Schaefer
published in: Journal of Computational and Applied Mathematics
publication date: 1990-01-01T00:00:00Z
review text: The following algorithm is proposed for linear parabolic equations on a bounded domain. A spatial discretization is introduced to get a method of lines, producing a system of ordinary differential equations, \(u_ t=- Lu+b.\) For a given time step \(\Delta\), an ellipse enclosing the spectrum of \(\Delta\) L is found, and on this ellipse the operator \((\Delta L)^{- 1}(e^{\Delta L}-1)\) is approximated by a finite expansion in terms of Chebychev polynomials. This expansion then serves to generate a pseudospectral method for the method of lines. The method is compared with an alternating-direction method and a locally one-dimensional method on a number of problems.
Mathematics Subject Classification ID: 65N35
Mathematics Subject Classification ID: 65N40
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65Y05
Mathematics Subject Classification ID: 35K20
zbMATH DE Number: 4124958
zbMATH Keywords: ADI/LOD methods
zbMATH Keywords: finite differences
zbMATH Keywords: implicit methods
zbMATH Keywords: iterative methods
zbMATH Keywords: \(L_ 0\)-stability
zbMATH Keywords: least squares approximation
zbMATH Keywords: semi-discrete equations
zbMATH Keywords: sparse linear systems
zbMATH Keywords: algorithm
zbMATH Keywords: method of lines
zbMATH Keywords: finite expansion
zbMATH Keywords: Chebychev polynomials
zbMATH Keywords: pseudospectral method
zbMATH Keywords: alternating-direction method
reviewed by: Gerald W. Hedstrom
describes a project that uses: LSQR
describes a project that uses: CHEBYCODE
describes a project that uses: CRAIG
MaRDI profile type: Publication
full work available at URL: 0377-0427(90)90193-4
OpenAlex ID: W2054370002
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description: scientific article; zbMATH DE number 4124958