The Levenberg–Marquardt regularization for the backward heat equation with fractional derivative. ETNA - Electronic Transactions on Numerical Analysis
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2 juin 2022
- handle: 10670/1.bzuvkv
- issn: 1068-9613
- doi: 10.1553/etna_vol57s67
info:eu-repo/semantics/openAccess
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Christine Böckmann et al., « The Levenberg–Marquardt regularization for the backward heat equation with fractional derivative. ETNA - Electronic Transactions on Numerical Analysis », Elektronisches Publikationsportal der Österreichischen Akademie der Wissenschafte, ID : 10.1553/etna_vol57s67
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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.