An inverse Sturm–Liouville problem with a fractional derivative

Bangti Jin; William Rundell

doi:10.1016/j.jcp.2012.04.005

An inverse Sturm–Liouville problem with a fractional derivative

Bangti Jin, William Rundell

Research output: Contribution to journal › Article › peer-review

35 Scopus citations

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.

Original language	English (US)
Pages (from-to)	4954-4966
Number of pages	13
Journal	Journal of Computational Physics
Volume	231
Issue number	14
DOIs	https://doi.org/10.1016/j.jcp.2012.04.005
State	Published - May 2012
Externally published	Yes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-C1-016-04
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.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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10.1016/j.jcp.2012.04.005

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title = "An inverse Sturm–Liouville problem with a fractional derivative",

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. {\textcopyright} 2012 Elsevier Inc.",

author = "Bangti Jin and William Rundell",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): KUS-C1-016-04 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. This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

year = "2012",

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doi = "10.1016/j.jcp.2012.04.005",

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N2 - 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.

AB - 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.

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JO - Journal of Computational Physics

JF - Journal of Computational Physics

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ER -

An inverse Sturm–Liouville problem with a fractional derivative

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