Accurate computation of higher Sturm-Liouville eigenvalues
type: Item
instance of: scholarly article
title: Accurate computation of higher Sturm-Liouville eigenvalues
zbMATH Open document ID: 0707.65059
DOI: 10.1007/BF01385778
author: G. Vanden Berghe
author: H. De Meyer
published in: Numerische Mathematik
publication date: 1992-06-25T00:00:00Z
full work available at URL: https://eudml.org/doc/133547
review text: The computation of eigenvalues of regular Sturm-Liouville problems is considered. It is shown that a simple step-dependent linear multistep method can be used to reduce the error of the order \(k^ 4h^ 2\) of the centered finite difference estimate of the k-th eigenvalue with uniform step length h, to an error of order \(kh^ 2\). By an appropriate minimization of the local error term of the method one can obtain even more accurate results. A comparison of the simple correction techniques of \textit{J. W. Paine}, \textit{F. R. de Hoog}, and \textit{R. S. Anderssen} [Computing 26, 123--135 (1981; Zbl 0436.65063)] and of \textit{A. L. Andrew} and \textit{J. W. Paine} [Numer. Math. 50, 205--215 (1986; Zbl 0588.65062)] is given. Numerical examples demonstrate the usefulness of this correction even for low values of \(k\).
reviewed by: G. Vanden Berghe
Mathematics Subject Classification ID: 65L15
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L70
Mathematics Subject Classification ID: 34L15
zbMATH DE Number: 990
zbMATH Keywords: eigenvalues
zbMATH Keywords: regular Sturm-Liouville problems
zbMATH Keywords: linear multistep method
zbMATH Keywords: centered finite difference estimate
zbMATH Keywords: minimization of the local error term
MaRDI profile type: Publication
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OpenAlex ID: W2081535739
description: scientific article; zbMATH DE number 990