An inverse Sturm-Liouville problem with a fractional derivative

Authors:
Bangti Jin;William Rundell
Affiliations:
Department of Mathematics and Institute for Applied Mathematics and Computational Science, Texas A&M University, College Station, TX 77843-3368, USA;Department of Mathematics and Institute for Applied Mathematics and Computational Science, Texas A&M University, College Station, TX 77843-3368, USA
Venue:
Journal of Computational Physics
Year:
2012

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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 @a@?(1,2) of fractional derivative is sufficiently away from 2.