An inverse Sturm–Liouville problem with a fractional derivative

Bangti Jin, William Rundell

Research output: Contribution to journalArticlepeer-review

22 Scopus citations

Abstract

In this paper, we numerically investigate an inverse problem of recovering the potential term in a fractional Sturm-Liouville problem from one spectrum. The qualitative behaviors of the eigenvalues and eigenfunctions are discussed, and numerical reconstructions of the potential with a Newton method from finite spectral data are presented. Surprisingly, it allows very satisfactory reconstructions for both smooth and discontinuous potentials, provided that the order . α∈. (1,. 2) of fractional derivative is sufficiently away from 2. © 2012 Elsevier Inc.
Original languageEnglish (US)
Pages (from-to)4954-4966
Number of pages13
JournalJournal of Computational Physics
Volume231
Issue number14
DOIs
StatePublished - May 2012
Externally publishedYes

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