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. (C) 2014 Elsevier B.V. All rights reserved.