Numerical computation of eigenvalues in spectral gaps of Sturm-Liouville operators
type: Item
instance of: scholarly article
title: Numerical computation of eigenvalues in spectral gaps of Sturm-Liouville operators
zbMATH Open document ID: 1104.65080
published in: Journal of Computational and Applied Mathematics
publication date: 2006-03-24T00:00:00Z
review text: The numerical calculation of the eigenvalues of a singular Sturm-Liouville problem \(-y'' + Q(x)y = \lambda y, x \in R+\), is studied in the case that the potential \(Q\) is a decaying \(L_1\) perturbation of a periodic function. Hence its essential spectrum has a band-gap structure. Two approaches are considered. One uses a shooting method, the other one an algebraic technique which is based on a theorem by \textit{G. Stolz} and \textit{J. Weidmann} [J. Reine Angew. Math. 445, 31--44 (1993; Zbl 0781.34052)]. Both approaches are capable of generating approximations to eigenvalues inside any gap of the essential spectrum. They do not generate spurious eigenvalues. Two examples with numerical ressults are given.
Mathematics Subject Classification ID: 65L15
Mathematics Subject Classification ID: 34L16
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 34B24
zbMATH DE Number: 5015145
zbMATH Keywords: Sturm-Liouville operator
zbMATH Keywords: eigenvalue problem
zbMATH Keywords: spectral gap
zbMATH Keywords: numerical examples
zbMATH Keywords: essential spectrum
zbMATH Keywords: shooting method
author: Lidia Aceto
author: Paolo Ghelardoni
author: Marco Marletta
reviewed by: Ludwig Elsner
MaRDI profile type: Publication
full work available at URL: j.cam.2005.01.008
OpenAlex ID: W2056196261
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DOI: 10.1016/J.CAM.2005.01.008
description: scientific article; zbMATH DE number 5015145