Boundary Value Methods for the reconstruction of Sturm-Liouville potentials

Lidia Aceto, Paolo Ghelardoni, Cecilia Magherini

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper we present numerical procedures for solving the two inverse Sturm-Liouville problems known in the literature as the two-spectra and the half inverse problems. The method proposed looks for a continuous approximation of the unknown potential belonging to a suitable function space of finite dimension. In order to compute such an approximation a sequence of direct problems has to be solved. This is done by applying one of the Boundary Value Methods, generalizing the classical Numerov scheme, recently introduced by the authors. Numerical results confirming the effectiveness of the approach proposed are also reported.

Original languageEnglish
Pages (from-to)2960-2974
Number of pages15
JournalApplied Mathematics and Computation
Volume219
Issue number6
DOIs
Publication statusPublished - 25 Nov 2012
Externally publishedYes

Keywords

  • Boundary Value Methods
  • Eigenvalues
  • Inverse Sturm-Liouville problems

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