Stability of a Chebychev pseudospectral solution of the wave equation with absorbing boundaries
type: Item
instance of: scholarly article
title: Stability of a Chebychev pseudospectral solution of the wave equation with absorbing boundaries
zbMATH Open document ID: 0898.65058
DOI: 10.1016/S0377-0427(97)00192-1
published in: Journal of Computational and Applied Mathematics
publication date: 1998-11-01T00:00:00Z
review text: As it is known the continuous one-dimensional problem with one absorbing boundary and one Dirichlet boundary has been shown to be far from normal and the spectrum of that problem says little about the stability behavior of the solution. In this paper, the presented analysis proves that the discrete formulation with Dirichlet boundaries at all boundaries is nearly normal. The near-normality follows from the near-normality of the second-order derivative pseudospectral differential operator. Numerical results confirm the predicted values on allowable timesteps obtained from a spectral analysis, for both Chebyshev and modified-Chebyshev implementations.
Mathematics Subject Classification ID: 65M70
Mathematics Subject Classification ID: 35L05
Mathematics Subject Classification ID: 65M12
zbMATH DE Number: 1121352
zbMATH Keywords: Chebyshev pseudospectral method
zbMATH Keywords: wave equation
zbMATH Keywords: absorbing boundaries
zbMATH Keywords: stability
author: R. A. Renaut
reviewed by: V. V. Strygin
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1121352