High-order numerical method for two-dimensional Riesz space fractional advection-dispersion equation.

In this paper, by combining of fractional centered dierence ap- proach with alternating direction implicit method, we introduce a mixed dif- ference method for solving two-dimensional Riesz space fractional advection- dispersion equation. The proposed method is a fourth order centered dierence operator in spatial directions and second order Crank-Nicolson method in tem- poral direction. By reviewing the consistency and stability of the method, the convergence of the proposed method is achieved. Several numerical examples are considered aiming to demonstrate the validity and applicability of the pro- posed technique.