An inverse Sturm–Liouville problem with a fractional derivative

Handle URI:
http://hdl.handle.net/10754/597537
Title:
An inverse Sturm–Liouville problem with a fractional derivative
Authors:
Jin, Bangti; Rundell, William
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.
Publisher:
Elsevier BV
Journal:
Journal of Computational Physics
KAUST Grant Number:
KUS-C1-016-04
Issue Date:
May-2012
DOI:
10.1016/j.jcp.2012.04.005
Type:
Article
ISSN:
0021-9991
Sponsors:
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.
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorJin, Bangtien
dc.contributor.authorRundell, Williamen
dc.date.accessioned2016-02-25T12:41:39Zen
dc.date.available2016-02-25T12:41:39Zen
dc.date.issued2012-05en
dc.identifier.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.en
dc.identifier.issn0021-9991en
dc.identifier.doi10.1016/j.jcp.2012.04.005en
dc.identifier.urihttp://hdl.handle.net/10754/597537en
dc.description.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.en
dc.description.sponsorshipThis 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.en
dc.publisherElsevier BVen
dc.subjectFractional differential equationen
dc.subjectInverse problemen
dc.subjectMittag-Leffler functionen
dc.subjectSturm-Liouville problemen
dc.titleAn inverse Sturm–Liouville problem with a fractional derivativeen
dc.typeArticleen
dc.identifier.journalJournal of Computational Physicsen
dc.contributor.institutionTexas A and M University, College Station, United Statesen
kaust.grant.numberKUS-C1-016-04en
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