A spectral Galerkin approximation of the Orr-Sommerfeld eigenvalue problem in a semi-infinite domain
type: Item
instance of: scholarly article
title: A spectral Galerkin approximation of the Orr-Sommerfeld eigenvalue problem in a semi-infinite domain
zbMATH Open document ID: 0791.65061
DOI: 10.1007/BF01385692
author: Thomas M. Fischer
published in: Numerische Mathematik
publication date: 1994-07-07T00:00:00Z
full work available at URL: https://eudml.org/doc/133757
review text: The convergence of a Galerkin approximation of the Orr-Sommerfeld eigenvalue problem, which is defined in a semi-infinite domain, is studied theoretically. In case the system of trial functions is based on a composite of Jacobi polynomials and an exponential transform of the semi-infinite domain, the error of the Galerkin approximation is estimated in terms of the transformation parmeter \(a\) and the number \(N\) of trial functions. Finite or infinite-order convergence of the spectral Galerkin method is obtained depending on how the transformation parameter is chosen. If the transformation parameter is fixed, then convergence is of finite order only. However, if \(a\) is varied proportional to \(1/N^ \rho\) with an exponent \(0<\rho<1\), then the approximate eigenvalue converges faster than any finite power of \(1/N\) as \(N \to \infty\). Some numerical examples are given.
Mathematics Subject Classification ID: 65L15
Mathematics Subject Classification ID: 65L60
Mathematics Subject Classification ID: 76D10
Mathematics Subject Classification ID: 34L40
Mathematics Subject Classification ID: 34L15
zbMATH DE Number: 569179
zbMATH Keywords: Orr-Sommerfeld eigenvalue problem
zbMATH Keywords: convergence
zbMATH Keywords: spectral Galerkin method
zbMATH Keywords: numerical examples
MaRDI profile type: Publication
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OpenAlex ID: W1977794418
description: scientific article; zbMATH DE number 569179