Solutions of Direct and Inverse Even-Order Sturm-Liouville Problems Using Magnus Expansion
- In this paper Lie group method in combination with Magnus expansion is utilized to develop a universal method applicable to solving a Sturm–Liouville problem (SLP) of any order with arbitrary boundary conditions. It is shown that the method has ability to solve direct regular (and some singular) SLPs of even orders (tested for up to eight), with a mix of (including non-separable and finite singular endpoints) boundary conditions, accurately and efficiently. The present technique is successfully applied to overcome the difficulties in finding suitable sets of eigenvalues so that the inverse SLP problem can be effectively solved. The inverse SLP algorithm proposed by Barcilon (1974) is utilized in combination with the Magnus method so that a direct SLP of any (even) order and an inverse SLP of order two can be solved effectively.
| Author details: | Upeksha PereraORCiD, Christine BöckmannORCiD |
|---|---|
| DOI: | https://doi.org/10.3390/math7060544 |
| ISSN: | 2227-7390 |
| Title of parent work (English): | Mathematics |
| Publisher: | MDPI |
| Place of publishing: | Basel, Schweiz |
| Publication type: | Article |
| Language: | English |
| Date of first publication: | 2019/06/14 |
| Publication year: | 2019 |
| Release date: | 2023/07/14 |
| Tag: | Magnus expansion; higher-order Sturm–Liouville problems; inverse Sturm–Liouville problems |
| Volume: | 7 |
| Issue: | 6 |
| Article number: | 544 |
| Number of pages: | 24 |
| 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 |
| License (German): |  CC-BY - Namensnennung 4.0 International |
| External remark: | Zweitveröffentlichung in der Schriftenreihe Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe ; 1336 |
