Approximation properties of a mapped Chebyshev method
type: Item
instance of: scholarly article
title: Approximation properties of a mapped Chebyshev method
zbMATH Open document ID: 0973.65086
DOI: 10.1016/S0168-9274(99)00017-3
author: M. R. Abril-Raymundo
author: Bosco García-Archilla
published in: Applied Numerical Mathematics
publication date: 2001-11-15T00:00:00Z
review text: A mapped Chebyshev technique introduced by \textit{D. Kosloff} and \textit{H. Tal-Ezer} [J. Comput. Phys. 104, No. 2, 457-469 (1993; Zbl 0781.65082)] is analyzed. For suitable choices of parameters the mapped Chebyshev methods yield better approximation results for derivatives than the standard collocation method. Error bounds are presented which show that for the parameters suggested in the literature a low order of approximation occurs. However, this observation only appears for levels of accuracy much more stringent than those in usual computations.
Mathematics Subject Classification ID: 65M70
Mathematics Subject Classification ID: 65M15
Mathematics Subject Classification ID: 35L45
zbMATH DE Number: 1398453
zbMATH Keywords: spectral methods
zbMATH Keywords: mapped Chebyshev methods
zbMATH Keywords: collocation method
zbMATH Keywords: error bounds
reviewed by: Wilhelm Heinrichs
MaRDI profile type: Publication
full work available at URL: s0168-9274(99)00017-3
OpenAlex ID: W2037298008
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description: scientific article; zbMATH DE number 1398453