An inverse Sturm-Liouville problem with a fractional derivative
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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 . . (1,. 2) of fractional derivative is sufficiently away from 2. 2012 Elsevier Inc.
JOURNAL OF COMPUTATIONAL PHYSICS
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Jin, Bangti||Rundell, William