KAUST Grant NumberKUS-C1-016-04
Permanent link to this recordhttp://hdl.handle.net/10754/597537
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AbstractIn 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.
CitationJin 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.
SponsorsThis 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.
JournalJournal of Computational Physics