带Robin边界条件的分数阶对流-扩散方程的数值解法

Numerical methods of the fractional advection-dispersion equation with Robin boundary condition

摘要:

本文对带Robin边界条件的分数阶对流-扩散方程进行了数值研究.利用移位Grünwald公式对Riemann-Liouville空间分数阶导数进行离散，在此基础上建立一种隐式有限差分格式，讨论了它差分解的存在唯一性；然后分析了该格式的相容性、稳定性和收敛性；最后通过数值算例验证格式是可靠和有效的.

Abstract:

In this paper, we study the practical numerical methods to solve the fractional advection-dispersion equation with Robin boundary condition. We propose an implicit finite difference scheme based on the shifted Grünwald formula to discretize Riemann-Liouville fractional derivative. Existence and uniqueness of numerical solutions are derived. It is proved that the implicit finite difference scheme is unconditionally stable and convergent. Finally, numerical simulations show that the method is efficient.