Inverse Sturm-Liouville problems with pseudospectral methods

Date

2015-07-03

Author

Altundag, H.
Boeckmann, C.
Taşeli, Hasan

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In this paper a technique to obtain a first approximation for singular inverse Sturm-Liouville problems with a symmetrical potential is introduced. The singularity, as a result of unbounded domain (-infinity, infinity), is treated by considering numerically the asymptotic limit of the associated problem on a finite interval (-L, L). In spite of this treatment, the problem has still an ill-conditioned structure unlike the classical regular ones and needs regularization techniques. Direct computation of eigenvalues in iterative solution procedure is made by means of pseudospectral methods. A fairly detailed description of the numerical algorithm and its applications to specific examples are presented to illustrate the accuracy and convergence behaviour of the proposed approach.

Subject Keywords

31A25, 65F18, Regularization Method, Condition Number, Pseudospectral Method, Regular And Singular İnverse Sturm-Liouville Problems

URI

https://hdl.handle.net/11511/48827

Journal

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS

DOI

https://doi.org/10.1080/00207160.2014.939646

Collections

Department of Mathematics, Article

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Citation Formats

H. Altundag, C. Boeckmann, and H. Taşeli, “Inverse Sturm-Liouville problems with pseudospectral methods,” INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, pp. 1373–1384, 2015, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/48827.