分数阶对流-弥散方程的有限差分方法

Finite difference approximations for fractional advection-dispersion eqution

本文对分数阶对流-弥散方程的初边值问题进行了数值研究.我们采用移位Grun-wald公式对空间分数阶导数进行离散,在此基础上建立Crank-Nichonlson(简称C-N)差分格式,并讨论了差分解的存在唯一性,然后分析了该方法的稳定性及收敛性,并利用外推法提高收敛阶.数值算例验证了格式的有效性.

In this paper, we study the practical numercial methods to slove the fractional advection-dispersion equation. We propose a C-N method based on the shifted Grunwald formula. Existence and unique- ness of numercal solutions are derived. It is proved that the C-N scheme is unconditionally stable and convergent. Extrapolation method is used to obtain higher accuracy. Numerical simulations show that the method is efficient.