Corrected finite difference eigenvalues of periodic Sturm-Liouville problems
type: Item
instance of: scholarly article
title: Corrected finite difference eigenvalues of periodic Sturm-Liouville problems
zbMATH Open document ID: 0930.65089
DOI: 10.1016/S0168-9274(98)00093-2
author: D. J. Condon
published in: Applied Numerical Mathematics
publication date: 2000-02-09T00:00:00Z
review text: Finite element approximation to eigenvalues of regular Sturm-Liouville equations \(-y''+qy=\lambda y\) can be improved applying a technique proposed by \textit{J. W. Paine}, \textit{F. R. de Hoog} and \textit{R. S. Anderssen} [Computing 26, 123-139 (1981; Zbl 0445.65087)] in the case of boundary conditions \(y(0)=y(\pi)=0\). In the present article periodic boundary conditions \(y(0)=y(\pi)\), \(y'(0)=y'(\pi)\) are considered. The author shows that a proof similar to that given by \textit{A. L. Andrew} [J. Aust. Math. Soc., Ser. B 30, No. 4, 460-469 (1989; Zbl 0676.65089)] can be used to prove that the correction technique applied to a finite difference scheme given by \textit{G. Vanden Berghe}, \textit{M. Van Daele} and \textit{H. De Meyer} [Appl. Numer. Math. 18, No. 1-3, 69-78 (1995; Zbl 0834.65075)] reduces the error in the \(k\)-th eigenvalue estimate from \(O(k^4h^2)\) to \(O(kh^2)\), where \(h\) is the uniform mesh length.
Mathematics Subject Classification ID: 65L15
Mathematics Subject Classification ID: 34L15
Mathematics Subject Classification ID: 65L12
zbMATH DE Number: 1311343
zbMATH Keywords: periodic Sturm-Liouville problems
zbMATH Keywords: finite element
zbMATH Keywords: correction technique
zbMATH Keywords: finite difference scheme
zbMATH Keywords: eigenvalue
reviewed by: Waldemar Velte
MaRDI profile type: Publication
full work available at URL: s0168-9274(98)00093-2
OpenAlex ID: W2089174004
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description: scientific article; zbMATH DE number 1311343