Inverse Sturm-Liouville problems with pseudospectral methods


Altundag H., Boeckmann C., TAŞELİ H.

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, cilt.92, ss.1373-1384, 2015 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 92 Konu: 7
  • Basım Tarihi: 2015
  • Doi Numarası: 10.1080/00207160.2014.939646
  • Dergi Adı: INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
  • Sayfa Sayıları: ss.1373-1384

Özet

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.