Eigenvalues of discontinuous Sturm-Liouville problems with symmetric potentials
type: Item
instance of: scholarly article
title: Eigenvalues of discontinuous Sturm-Liouville problems with symmetric potentials
zbMATH Open document ID: 0682.65054
DOI: 10.1016/0898-1221(89)90220-4
publication date: 1989-01-01T00:00:00Z
review text: The first 15 eigenvalues of two discontinuous Sturm-Liouville systems, \(- u''=\lambda u\) and \(-u''+(2 \cos 2x)u=\lambda u\) respectively, with boundary conditions \(u'(0)=u'(\pi)=0\) and symmetric jump conditions \(u(d_ 1+)=au(d_ 1-),\) \(u'(d_ 1+)=a^{-1}u'(d_ 1-)+bu(d_ 1-),\) \(u(d_ 2-)=au(d_ 2+),\quad u'(d_ 2-)=a^{-1}u'(d_ 2+)-bu(d_ 2- )\) were found by the classical fourth order Runge-Kutta method. The eigenvalues are plotted. The eigenvalues are used to reconstruct the potential function \(q=2 \cos 2x\) of the second Sturm-Liouville system by means of the author's algorithm [ibid. 18, No.4, 349-356 (1989; reviewed above)]. Then as the third example of the Sturm-Liouville system a symmetric potential function with symmetrically located discontinuities \(d_ 1\), \(d_ 2\) satisfying symmetric jump conditions is reconstructed by the same algorithm.
Mathematics Subject Classification ID: 65L15
Mathematics Subject Classification ID: 34L99
zbMATH DE Number: 4117779
zbMATH Keywords: eigenvalues
zbMATH Keywords: discontinuous Sturm-Liouville systems
zbMATH Keywords: fourth order Runge- Kutta method
zbMATH Keywords: potential function
zbMATH Keywords: discontinuities
zbMATH Keywords: symmetric jump conditions
author: Mei Kobayashi
MaRDI profile type: Publication
full work available at URL: 0898-1221(89)90220-4
OpenAlex ID: W2039400441
cites work: An algorithm for discontinuous inverse Sturm-Liouville problems with symmetric potentials
cites work: Q3779682
cites work: High order embedded Runge-Kutta formulae
cites work: The Inverse Sturm-Liouville Problem and the Rayleigh-Ritz Method
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 4117779