A new a posteriori parameter choice strategy for the convolution regularization of the space-fractional backward diffusion problem

Abstract

In this paper, we consider a backward space-fractional diffusion problem. We propose an a posteriori parameter choice rule for the regularization method given in Zheng and Wei (2010), where the authors proposed a regularization method called convolution regularization method, and gave an a priori parameter choice strategy. In this paper, we study the same problem but give a new a posteriori parameter choice based on a modified version of the discrepancy principle, and obtain a log-type error estimate under an additional source condition. Numerical results show that our method is feasible.