An inverse Sturm–Liouville problem with a fractional derivative
| dc.contributor.author | Jin, Bangti | |
| dc.contributor.author | Rundell, William | |
| dc.date.accessioned | 2016-02-25T12:41:39Z | |
| dc.date.available | 2016-02-25T12:41:39Z | |
| dc.date.issued | 2012-05 | |
| dc.identifier.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. | |
| dc.identifier.issn | 0021-9991 | |
| dc.identifier.doi | 10.1016/j.jcp.2012.04.005 | |
| dc.identifier.uri | http://hdl.handle.net/10754/597537 | |
| dc.description.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. | |
| dc.description.sponsorship | 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. | |
| dc.publisher | Elsevier BV | |
| dc.subject | Fractional differential equation | |
| dc.subject | Inverse problem | |
| dc.subject | Mittag-Leffler function | |
| dc.subject | Sturm-Liouville problem | |
| dc.title | An inverse Sturm–Liouville problem with a fractional derivative | |
| dc.type | Article | |
| dc.identifier.journal | Journal of Computational Physics | |
| dc.contributor.institution | Texas A and M University, College Station, United States | |
| kaust.grant.number | KUS-C1-016-04 |