TY - JOUR
T1 - An inverse Sturm–Liouville problem with a fractional derivative
AU - Jin, Bangti
AU - Rundell, William
N1 - 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.
PY - 2012/5
Y1 - 2012/5
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.
UR - http://hdl.handle.net/10754/597537
UR - https://linkinghub.elsevier.com/retrieve/pii/S0021999112001763
UR - http://www.scopus.com/inward/record.url?scp=84861231247&partnerID=8YFLogxK
U2 - 10.1016/j.jcp.2012.04.005
DO - 10.1016/j.jcp.2012.04.005
M3 - Article
SN - 0021-9991
VL - 231
SP - 4954
EP - 4966
JO - Journal of Computational Physics
JF - Journal of Computational Physics
IS - 14
ER -