HIGH-ORDER NUMERICAL METHOD FOR TWO-DIMENSIONAL RIESZ SPACE FRACTIONAL ADVECTION-DISPERSION EQUATION

1. Introduction. Many researchers focused on fractional partial differential equations due to their useful applications in many real-world models, modeling with the least error and overlapping physically with scientific issues. Fractional partial differential equations are mainly classified to the time, space, and time-space fractional partial differential equations. Of all these types, space fractional partial differential equations are containing fractional diffusion equation, ABSTRACT In this paper, by combining of fractional centered difference approach with alternating direction implicit method, we introduce a mixed difference method for solving two-dimensional Riesz space fractional advectiondispersion equation. The proposed method is a fourth order centered difference operator in spatial directions and second order Crank-Nicolson method in temporal 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 proposed technique.