Tikhonov-type regularization method for a sideways problem of the time-fractional diffusion equation

Abstract

A sideways problem of the time-fractional diffusion equation is investigated. The solution of this problem does not depend on the given data. In view of this, this article uses a Tikhonov-type regularized method to construct an approximate solution and overcome the ill-posedness of considered problem. The a-posteriori convergence estimates of logarithmic and double logarithmic types for the regularized method are derived. Finally, for smooth and non-smooth cases we respectively verify the effectiveness of proposed method by doing the coresponding numerical experiments.

Keywords

• sideways problem
• time-fractional diffusion equation
• tikhonov-type regularization method
• a-posteriori convergence estimate
• numerical implementation