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 . . (1,. 2) of fractional derivative is sufficiently away from 2. 2012 Elsevier Inc.

authors

• Rundell, William

published proceedings

• JOURNAL OF COMPUTATIONAL PHYSICS

author list (cited authors)

• Jin, B., & Rundell, W.

citation count

• 25

complete list of authors

• Jin, Bangti||Rundell, William

publication date

• January 2012

publisher

• Elsevier  Publisher

published in

• Journal of Computational Physics  Journal

keywords

• Fractional Differential Equation
• Inverse Problem
• Mittag-leffler Function
• Sturm-liouville Problem

Digital Object Identifier (DOI)

• 10.1016/j.jcp.2012.04.005

start page

• 4954

end page

• 4966

volume

• 231

issue

• 14

URL

• http%3A%2F%2Fdx.doi.org%2F10.1016%2Fj.jcp.2012.04.005