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

作　　者：曾宝思 尹修草[1] 谢常平 房少梅[1] 

机构地区：[1]华南农业大学数学与信息学院,广州510642

出　　处：《四川大学学报（自然科学版）》2018年第1期13-17,共5页Journal of Sichuan University(Natural Science Edition)

基　　金：国家自然科学基金(11271141)

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.本文利用移位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,并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.In this paper, we consider numerical methods to solve the fractional advection-dispersion equa- tion with Robin boundary condition. We propose an implicit finite difference scheme based on the shifted Grunwald formula to discretize Riemann-Liouville fractional derivative. Existence and uniqueness of nu- merical solutions are derived. It is proved that the implicit finite difference scheme is unconditionally sta- ble and convergent. Finally, numerical simulations show that the method is efficient.

关 键 词：分数阶对流-扩散方程 Robin边界 隐式有限差分格式 稳定性 收敛性 

分 类 号：O241.82[理学—计算数学]