Inverse Sturm-Liouville problems with pseudospectral methods

Altundag H., Boeckmann C., TAŞELİ H.

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, vol.92, no.7, pp.1373-1384, 2015 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 92 Issue: 7
  • Publication Date: 2015
  • Doi Number: 10.1080/00207160.2014.939646
  • Journal Name: INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1373-1384
  • Keywords: 31A25, 65F18, regularization method, condition number, pseudospectral method, regular and singular inverse Sturm-Liouville problems, ILL-POSED PROBLEMS, POTENTIALS, RECONSTRUCTION, REGULARIZATION, SPECTRUM, EQUATION
  • Middle East Technical University Affiliated: Yes

Abstract

In this paper a technique to obtain a first approximation for singular inverse Sturm-Liouville problems with a symmetrical potential is introduced. The singularity, as a result of unbounded domain (-infinity, infinity), is treated by considering numerically the asymptotic limit of the associated problem on a finite interval (-L, L). In spite of this treatment, the problem has still an ill-conditioned structure unlike the classical regular ones and needs regularization techniques. Direct computation of eigenvalues in iterative solution procedure is made by means of pseudospectral methods. A fairly detailed description of the numerical algorithm and its applications to specific examples are presented to illustrate the accuracy and convergence behaviour of the proposed approach.