期刊
SIAM JOURNAL ON NUMERICAL ANALYSIS
卷 42, 期 5, 页码 1862-1874出版社
SIAM PUBLICATIONS
DOI: 10.1137/030602666
关键词
fractional diffusion equation; von Neumann stability analysis; parabolic integrodifferential equations; finite difference methods
A numerical method for solving the fractional diffusion equation, which could also be easily extended to other fractional partial differential equations, is considered. In this paper we combine the forward time centered space (FTCS) method, well known for the numerical integration of ordinary diffusion equations, with the Grunwald-Letnikov discretization of the Riemann-Liouville derivative to obtain an explicit FTCS scheme for solving the fractional diffusion equation. The stability analysis of this scheme is carried out by means of a powerful and simple new procedure close to the well-known von Neumann method for nonfractional partial differential equations. The analytical stability bounds are in excellent agreement with numerical test. A comparison between exact analytical solutions and numerical predictions is made.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据