中文摘要：

<正>1引言在古典的微分方程中,利用阶数为实数的分数阶导数代替整数阶导数,能更好地模拟许多物理现象.特别是具有复杂结构的多孔介质中的反常扩散问题.近年来分数阶微分方程在很多科学工程领域得到了广泛的应用[4,6,7,9].作为分数阶微分方程的一种,分数阶对流-扩散方程在物理学和地下水文学研究中已被用来模拟多孔介质中流体的流动情

英文摘要：

In this paper, we consider a two-dimensional fractional advectiondispersion equation （2D-FADE） with variable coefficients on a finite domain. We adopt the Grunwald-Letnikov definition of fractional derivative, and propose a fia,ctional Peaceman-Rachford scheme based on the alternating direction ethod for 2D-FADE. The stability and convergence of the fractional Peaccman-Rachford scheme are proved. A method is combined with spatial extrapolation to obtain temporally and spatially second order accurate numerical method. Some numerical examples are presented to support our theoretical analysis.