Solutions of Sturm-Liouville problems
- This paper further improves the Lie group method with Magnus expansion proposed in a previous paper by the authors, to solve some types of direct singular Sturm-Liouville problems. Next, a concrete implementation to the inverse Sturm-Liouville problem algorithm proposed by Barcilon (1974) is provided. Furthermore, computational feasibility and applicability of this algorithm to solve inverse Sturm-Liouville problems of higher order (for n=2,4) are verified successfully. It is observed that the method is successful even in the presence of significant noise, provided that the assumptions of the algorithm are satisfied. In conclusion, this work provides a method that can be adapted successfully for solving a direct (regular/singular) or inverse Sturm-Liouville problem (SLP) of an arbitrary order with arbitrary boundary conditions.
| Author details: | Upeksha PereraORCiDGND, Christine BöckmannORCiDGND |
|---|---|
| DOI: | https://doi.org/10.3390/math8112074 |
| ISSN: | 2227-7390 |
| Title of parent work (English): | Mathematics |
| Publisher: | MDPI |
| Place of publishing: | Basel |
| Publication type: | Article |
| Language: | English |
| Date of first publication: | 2020/11/20 |
| Publication year: | 2020 |
| Release date: | 2023/03/22 |
| Tag: | Sturm-Liouville problems of higher order; inverse Sturm-Liouville problems; problems; singular Sturm-Liouville |
| Volume: | 8 |
| Issue: | 11 |
| Article number: | 2074 |
| Number of pages: | 14 |
| Funding institution: | UNIVERSITY OF KELANIYA, SRI LANKA |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Peer review: | Referiert |
| Publishing method: | Open Access / Gold Open-Access |
| DOAJ gelistet | |
| License (German): |  CC-BY - Namensnennung 4.0 International |
