The Levenberg–Marquardt regularization for the backward heat equation with fractional derivative
- The backward heat problem with time-fractional derivative in Caputo's sense is studied. The inverse problem is severely ill-posed in the case when the fractional order is close to unity. A Levenberg-Marquardt method with a new a posteriori stopping rule is investigated. We show that optimal order can be obtained for the proposed method under a Hölder-type source condition. Numerical examples for one and two dimensions are provided.
| Author details: | Pornsarp PornsawadORCiDGND, Christine BöckmannORCiDGND, Wannapa Panitsupakamon |
|---|---|
| DOI: | https://doi.org/10.1553/etna_vol57s67 |
| ISBN: | 978-3-7001-8258-0 |
| ISSN: | 1068-9613 |
| Title of parent work (English): | Electronic transactions on numerical analysis - ETNA |
| Publisher: | Kent State University |
| Place of publishing: | Kent |
| Publication type: | Article |
| Language: | English |
| Date of first publication: | 2022/06/03 |
| Publication year: | 2022 |
| Release date: | 2024/06/03 |
| Tag: | Levenberg-Marquardt method; a posteriori stopping rule; backward heat problem; ill-posed problems; optimal order; time-fractional derivative |
| Volume: | 57 |
| Number of pages: | 13 |
| First page: | 67 |
| Last Page: | 79 |
| Funding institution: | Faculty of Science, Silpakorn University, Thailand [SRIF-JRG-2563-01] |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Peer review: | Referiert |
