Inverse Sturm-Liouville problems with pseudospectral methods

2015-07-03
Altundag, H.
Boeckmann, C.
Taşeli, Hasan
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.

Citation Formats
H. Altundag, C. Boeckmann, and H. Taşeli, “Inverse Sturm-Liouville problems with pseudospectral methods,” INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, vol. 92, no. 7, pp. 1373–1384, 2015, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/48827.