The Levenberg–Marquardt regularization for the backward heat equation with fractional derivative

Electronic Transactions on Numerical Analysis

article

Pornsarp Pornsawad¹  Christine Böckmann³  Wannapa Panitsupakamon¹ 

[1] Department of Mathematics, Faculty of Science, Silpakorn University;Centre of Excellence in Mathematics, Mahidol University;Institute of Mathematics, University of Potsdam;Helmholtz Centre for Polar and Marine Research, Alfred Wegener Institute

关键词: ill-posed problems;    time-fractional derivative;    backward heat problem;    Levenberg–Marquardt method;    a posteriori stopping rule;    optimal order;   

DOI  :  10.1553/etna_vol57s67

学科分类：数学（综合）

来源: Kent State University * Institute of Computational Mathematics

【 摘 要 】

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.

【 授权许可】

Unknown