Solving the Riesz–Feller space-fractional backward diffusion problem by a generalized Tikhonov method

Abstract

Abstract The article investigates a Riesz–Feller space-fractional backward diffusion problem. We develop a generalized Tikhonov regularization method to overcome the ill-posedness of this problem, and then based on the result of conditional stability, we derive the convergence estimates of logarithmic and double logarithmic types for the regularized method by adopting a-posteriori choice rules of regularization parameter. Finally, by using the finite difference method, we solve a direct problem to construct the data, and some corresponding results of numerical simulations are presented to verify the convergence and stability for this method.

Keywords

• Ill-posed problem
• Riesz–Feller space-fractional backward diffusion problem
• Regularization method
• A-posteriori convergence estimate
• Numerical simulation