A fast fourth-order scheme and its extrapolations for two-dimensional space fractional diffusion equations

This paper focuses on developing an efficient numerical method for solving two-dimensional Riemann-Liouville space fractional diffusion equations (SFDEs). The quasi-compact difference scheme is to discretize the SFDEs, and then the Richardson extrapolation method is employed to enhance the temporal accuracy to the fourth-order. Alternating direction implicit scheme is applied to decompose the problem into two linear systems. We introduce a fast Preconditioned Stable Bi-Conjugate Gradient algorithm to solve such systems. Moreover, we present the convergence theorem and the spectrum properties of the Strang preconditioner to show the computational efficiency. Finally, numerical experiments are conducted to validate the accuracy and robustness of our methods.