TY  - JOUR
A1  - Pornsawad, Pornsarp
A1  - Böckmann, Christine
A1  - Panitsupakamon, Wannapa
T1  - The Levenberg–Marquardt regularization for the backward heat equation with fractional derivative
T2  - Electronic transactions on numerical analysis - ETNA
N2  - 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.
KW  - ill-posed problems
KW  - time-fractional derivative
KW  - backward heat problem
KW  - Levenberg-Marquardt method
KW  - a posteriori stopping rule
KW  - optimal order
Y1  - 2022
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/63689
SN  - 978-3-7001-8258-0
SN  - 1068-9613
VL  - 57
SP  - 67
EP  - 79
PB  - Kent State University
CY  - Kent
ER  -