\(L_ 2\) estimates for Chebyshev collocation
type: Item
instance of: scholarly article
title: \(L_ 2\) estimates for Chebyshev collocation
zbMATH Open document ID: 0662.65101
DOI: 10.1007/BF01066480
published in: Journal of Scientific Computing
publication date: 1988-01-01T00:00:00Z
review text: Considering the numerical solution of symmetric hyperbolic systems with variable coefficients, the author proves a stability estimate for the following approach: From the hyperbolic system a system of ordinary differential equations is obtained by developing the solution into a Chebyshev series with N terms, projecting the spatial operator part and the right hand side in \(L_ 2\) onto the M-th degree Legendre polynomials \((M<N\) for smoothing), projecting then onto those polynomials which meet the boundary conditions. For \(N-M=cN^ r\), \(c>0\), \(1\geq r>0\) and for sufficiently smooth data the estimate converges to the estimate for the continuous system.
Mathematics Subject Classification ID: 65N35
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 35L20
Mathematics Subject Classification ID: 65N12
zbMATH DE Number: 4082905
zbMATH Keywords: Chebyshev collocation smoothing
zbMATH Keywords: symmetric hyperbolic systems
zbMATH Keywords: variable coefficients
zbMATH Keywords: stability
author: Luis G. M. Reyna
reviewed by: Gisbert Stoyan
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4082905