An inverse Sturm-Liouville problem with a fractional derivative

Details An inverse Sturm-Liouville problem with a fractional derivative An inverse Sturm-Liouville problem with a fractional derivative

2012-04-11

arxiv.org/abs/1204.2475v1

Mathematics

Numerical Analysis

16 pages, 6 figures, accepted for publication in Journal of Computational Physics

Scientific paper

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 $\alpha\in(1,2)$ of fractional derivative is sufficiently away from 2.

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