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Inverse Sturm-Liouville problems with pseudospectral methods
- 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.
| Author details: | Hüseyin Altundag, Christine BöckmannORCiDGND, Hasan Taseli |
|---|---|
| DOI: | https://doi.org/10.1080/00207160.2014.939646 |
| ISSN: | 0020-7160 |
| ISSN: | 1029-0265 |
| Title of parent work (English): | International journal of computer mathematics |
| Publisher: | Routledge, Taylor & Francis Group |
| Place of publishing: | Abingdon |
| Publication type: | Article |
| Language: | English |
| Year of first publication: | 2015 |
| Publication year: | 2015 |
| Release date: | 2017/03/27 |
| Tag: | 31A25; 65F18; condition number; pseudospectral method; regular and singular inverse Sturm-Liouville problems; regularization method |
| Volume: | 92 |
| Issue: | 7 |
| Number of pages: | 12 |
| First page: | 1373 |
| Last Page: | 1384 |
| Funding institution: | TUBITAK, the Scientific and Technical Research Council of Turkey |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| Peer review: | Referiert |
