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 advection-dispersion 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.

中文翻译：

---

二维Riesz空间分数阶对流-弥散方程的高阶数值方法

本文将分数中心差分法与交替方向隐式方法相结合，引入了一种求解二维Riesz空间分数阶对流-弥散方程的混合差分法。所提出的方法是空间方向上的四阶中心差分算子和时间方向上的二阶Crank-Nicolson方法。通过检查方法的一致性和稳定性，实现了所提出方法的收敛性。考虑了几个数值例子，旨在证明所提出技术的有效性和适用性。