Spectral collocation methods
type: Item
instance of: scholarly article
title: Spectral collocation methods
zbMATH Open document ID: 0671.65093
DOI: 10.1016/0168-9274(89)90033-0
author: David A. Kopriva
author: M. Yousuff Hussaini
author: Anthony T. Patera
published in: Applied Numerical Mathematics
publication date: 1989-01-01T00:00:00Z
full work available at URL: http://hdl.handle.net/2060/19870020353
review text: This is a survey article on the application of spectral collocation methods to the solution of partial differential equations. For the most part, the basis functions used are either trigonometric or Chebyshev polynomials, although there is some discussion of Legendre polynomials. In the first half of the article theoretical results on stability and accuracy are presented. No proofs are given, but there is adequate reference to the literature. The second half of the article is devoted to a discussion of considerations to be faced in the application of the methods to practical problems. Here the authors take up such questions as iterative methods and preconditioners for implicit versions of the method, smoothing methods to remove spurious oscillations near sharp gradients, and domain decomposition methods for complex geometries.
Mathematics Subject Classification ID: 65N35
Mathematics Subject Classification ID: 65-02
Mathematics Subject Classification ID: 35G30
zbMATH DE Number: 4098679
zbMATH Keywords: survey article
zbMATH Keywords: spectral collocation methods
zbMATH Keywords: Chebyshev polynomials
zbMATH Keywords: Legendre polynomials
zbMATH Keywords: stability
zbMATH Keywords: accuracy
zbMATH Keywords: iterative methods
zbMATH Keywords: preconditioners
zbMATH Keywords: smoothing methods
zbMATH Keywords: domain decomposition methods
reviewed by: Gerald W. Hedstrom
MaRDI profile type: Publication
OpenAlex ID: W2062869432
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description: scientific article; zbMATH DE number 4098679