A non-stationary iterative Tikhonov regularization method for simultaneous inversion in a time-fractional diffusion equation

Abstract

The present paper is devoted to recovering the source term and the initial data simultaneously for a time-fractional diffusion equation from additional temperature data at two fixed times t=T1 and t=T2. Firstly, we prove the uniqueness result for the direct problem. And then we apply a non-stationary iterative Tikhonov regularization method to solve the inverse problem and propose a finite dimensional approximation algorithm. Three numerical examples in both one-dimensional and two-dimensional cases are provided to demonstrate the effectiveness and feasibility of the proposed method.