An efficient iterative quasi-reversibility method for the inverse source problem of time-fractional diffusion equations

Abstract

This paper is devoted to recovering the source term for a time-fractional diffusion equation from additional temperature data at fixed time $t=1.$ We discuss a uniqueness result of the direct problem and the ill-posedness of the inverse problem, and then apply the iterative quasi-reversibility regularization method to solve the inverse problem. Finally, some one-dimensional and two-dimensional numerical examples are given to verify the effectiveness and feasibility of the proposed method.

Keywords:

• Error estimate
• inverse source problem
• iterative quasi-reversibility
• Morozov’s discrepancy principle

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The work described in this article was supported by the NNSF of China (12261082, 11326234), NSF of Gansu Province (145RJZA099), Scientific research project of Higher School in Gansu Province (2014A-012), and Project of NWNU-LKQN2020-08.