Finite difference methods for half inverse Sturm-Liouville problems
type: Item
instance of: scholarly article
title: Finite difference methods for half inverse Sturm-Liouville problems
zbMATH Open document ID: 1231.65124
author: Alan L. Andrew
published in: Applied Mathematics and Computation
publication date: 2011-10-11T00:00:00Z
review text: This paper extends the work of \textit{A. Kammanee} and \textit{C. Böckman} [Appl. Math. Comput. 214, No. 2, 342--352 (2009; Zbl 1170.65064)] in several ways. Only Dirichlet boundary conditions were considered in that paper, whereas this paper considers the boundary conditions \(y(0)=(\pi)=0, y(0)=y'(\pi)=0, y'(0)=y(\pi)=0, y'(0)=y'(\pi)=0\). This paper treats the generalized Hochstadt-Lieberman problem, using \(n\) eigenvalues and the values of \(q\) at \(m\) grid points with general \(m\) and \(n\), whereas that paper considered only the classical Hochstadt-Lieberman problem with \(m=n\). These methods use an asymptotic correction technique of Pain, deHoog and Anderson, and its extension to Numerov's method for various boundary conditions. In the classical case \(c=\dfrac{\pi}2\), Numerov's method is found to be particularly effective. Since eigenvalue data is scare in applications, the author also examines stability problems associated with the use of the extra information on \(q\) where \(c<\dfrac{\pi}2\) and give some suggestions for further research.
Mathematics Subject Classification ID: 65L15
zbMATH DE Number: 5956402
zbMATH Keywords: half-inverse Sturm
zbMATH Keywords: Liouville problem
reviewed by: R. S. Dahiya
MaRDI profile type: Publication
full work available at URL: j.amc.2011.05.085
OpenAlex ID: W2028042258
cites work: Inverse Eigenvalue Problems
cites work: Q4681781
cites work: Numerov's method for inverse Sturm–Liouville problems
cites work: Computing Sturm–Liouville potentials from two spectra
cites work: Q5708068
cites work: Q4277837
cites work: On the correction of finite difference eigenvalue approximations for Sturm-Liouville problems
cites work: On the correction of finite difference eigenvalue approximations for Sturm-Liouville problems with general boundary conditions
cites work: A Numerical Method for the Inverse Sturm–Liouville Problem
cites work: Small potential corrections for the discrete eigenvalues of the Sturm- Liouville problem
cites work: A finite-difference algorithm for an inverse Sturm-Liouville problem
cites work: Determination of partially known Sturm-Liouville potentials
cites work: Boundary value method for inverse Sturm-Liouville problems
cites work: Q3805818
cites work: Asymptotic correction of more Sturm-Liouville eigenvalue estimates.
cites work: Bvms for computing Sturm-Liouville symmetric potentials
cites work: Eine Umkehrung der Sturm-Liouvilleschen Eigenwertaufgabe. Bestimmung der Differentialgleichung durch die Eigenwerte
cites work: Q5802401
cites work: Q3790737
cites work: Solution of inverse nodal problems
cites work: Solving an inverse Sturm-Liouville problem by a Lie-group method
cites work: An Inverse Sturm–Liouville Problem with Mixed Given Data
cites work: Half-inverse spectral problems for Sturm–Liouville operators with singular potentials
cites work: Half-inverse problem for diffusion operators on the finite interval
cites work: Discontinuous inverse eigenvalue problems
cites work: Inverse spectral analysis with partial information on the potential, II. The case of discrete spectrum
cites work: Inverse spectral problems and closed exponential systems
cites work: Inverse spectral problem for a string equation with partial information
cites work: On the inverse resonance problem for Schrödinger operators
cites work: Q4745405
cites work: Damage detection and generalized Fourier coefficients
cites work: Q3446733
cites work: An inverse problem for the heat equation
cites work: Recovery of a Heat Equation by Four Measurements at One End
cites work: Correction of Numerov's eigenvalue estimates
cites work: Error bounds for the modified Newton's method
cites work: A convergence theorem for Newton-like methods in Banach spaces
cites work: Q4801273
cites work: On the eigenvalues of the Sturm-Liouville operator with potentials from Sobolev spaces
cites work: Efficient computation of high index Sturm-Liouville eigenvalues for problems in physics
cites work: Mapped barycentric Chebyshev differentiation matrix method for the solution of regular Sturm-Liouville problems
cites work: Inverse Sturm-Liouville problems: some recent developments
DOI: 10.1016/J.AMC.2011.05.085
description: scientific article; zbMATH DE number 5956402