Computing the spectral function for singular Sturm--Liouville problems
type: Item
instance of: scholarly article
title: Computing the spectral function for singular Sturm--Liouville problems
zbMATH Open document ID: 1064.65075
published in: Journal of Computational and Applied Mathematics
publication date: 2005-02-23T00:00:00Z
review text: Algorithms for computing Sturm-Liouville spectral density functions are developed based on several mathematical characterizations. Especially singular Sturm-Liouville problems of the form \[ -U''+q(x)U=\lambda U,\quad x\in [a,\infty) \] and \[ U(a)\cos\alpha +U'(a)\sin\alpha=0 \] are studied when \(q\) belongs to Weyl's limit point case and generates some continuous spectrum. Convergence and error bounds are derived and methods are tested on several examples. The results are compared with those from the existing software package SLEDGE.
reviewed by: G. Vanden Berghe
Mathematics Subject Classification ID: 65L15
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 65L70
Mathematics Subject Classification ID: 34L16
Mathematics Subject Classification ID: 34B24
zbMATH DE Number: 2137367
zbMATH Keywords: singular Sturm-Liouville problem
zbMATH Keywords: software package SLEDGE
zbMATH Keywords: spectral density function
zbMATH Keywords: spectral measure
zbMATH Keywords: Step function approximation
zbMATH Keywords: \(h^2\)-extrapolation
zbMATH Keywords: Mesh equidistribution
zbMATH Keywords: comparison of methods
zbMATH Keywords: numerical examples
zbMATH Keywords: convergence
zbMATH Keywords: error bounds
author: Charles T. Fulton
author: D. B. Pearson
author: Steven A. Pruess
describes a project that uses: SLEDGE
MaRDI profile type: Publication
full work available at URL: j.cam.2004.07.006
OpenAlex ID: W2040229264
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DOI: 10.1016/J.CAM.2004.07.006
description: scientific article; zbMATH DE number 2137367