Pornsawad P.Böckmann C.Panitsupakamon W.Mahidol University2023-06-182023-06-182022-01-01Electronic Transactions on Numerical Analysis Vol.57 (2022) , 67-79https://repository.li.mahidol.ac.th/handle/20.500.14594/85122The 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.MathematicsArticleSCOPUS10.1553/etna_vol57s672-s2.0-8513254130810689613