An inverse Sturm–Liouville problem with a fractional derivative

Type
Article

Authors
Jin, Bangti
Rundell, William

KAUST Grant Number
KUS-C1-016-04

Date
2012-05

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.

Citation
Jin B, Rundell W (2012) An inverse Sturm–Liouville problem with a fractional derivative. Journal of Computational Physics 231: 4954–4966. Available: http://dx.doi.org/10.1016/j.jcp.2012.04.005.

Acknowledgements
This work is supported by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST), and NSF Award DMS-0715060.

Publisher
Elsevier BV

Journal
Journal of Computational Physics

DOI
10.1016/j.jcp.2012.04.005

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