Optimal error bound and simplified Tikhonov regularization method for a backward problem for the time-fractional diffusion equation

In this paper, we consider a backward problem for a time-fractional diffusion equation. Such a problem is ill-posed. The optimal error bound for the problem under a source condition is analyzed. A simplified Tikhonov regularization method is utilized to solve the problem, and its convergence rates are analyzed under an a priori regularization parameter choice rule and an a posteriori regularization parameter choice rule, respectively. Numerical examples show that the proposed regularization method is effective and stable, and both parameter choice rules work well.