An adaptive pseudo-spectral method for reaction diffusion problems
type: Item
instance of: scholarly article
title: An adaptive pseudo-spectral method for reaction diffusion problems
zbMATH Open document ID: 0668.65092
DOI: 10.1016/0021-9991(89)90215-5
author: S. H. Smith
published in: Journal of Computational Physics
publication date: 1989-01-01T00:00:00Z
full work available at URL: metadc1093443
review text: An adaptive pseudo-spectral numerical method, solving systems of reaction, diffusion and convection equations is presented, which uses both Chebyshev and Galerkin approximations of the errors. The authors develop a family of functionals \(I_ r(u)\) with the property that the maximum norm of the error is bounded by \(I_ r(u)/J^ r\), where r is an integer and J is the degree of the polynomial approximation. These functionals are used in the adaptive procedure whereby the problem is dynamically transformed to minimize \(I_ r(u)\). The number of collocation points is then chosen to maintain a prescribed error bound. The method is llustrated by various examples from combustion problems in one and two dimensions. In the second section the authors describe the model and illustrate the features of the solution which make its numerical computation difficult. In section 3 the adaptive procedure is described and in the fourth section the functional which is used for the error estimation is given. In section 5 the authors illustrate the effectiveness of the proposed procedure by examples of the given model.
Mathematics Subject Classification ID: 65N35
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 80A25
zbMATH DE Number: 4094737
zbMATH Keywords: adaptive pseudo-spectral method
zbMATH Keywords: Chebyshev approximation
zbMATH Keywords: numerical examples
zbMATH Keywords: systems of reaction, diffusion and convection equations
zbMATH Keywords: Galerkin approximations
zbMATH Keywords: collocation
zbMATH Keywords: error bound
zbMATH Keywords: combustion problems
zbMATH Keywords: error estimation
MaRDI profile type: Publication
OpenAlex ID: W1994206529
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description: scientific article; zbMATH DE number 4094737