Computer Science – Numerical Analysis
Scientific paper
2003-11-10
SIAM J. Numer. Anal. Vol. 42, No. 5, pp. 1862--1874 (2005)
Computer Science
Numerical Analysis
22 pages, 6 figures
Scientific paper
10.1137/030602666
A numerical method to solve the fractional diffusion equation, which could also be easily extended to many other fractional dynamics equations, is considered. These fractional equations have been proposed in order to describe anomalous transport characterized by non-Markovian kinetics and the breakdown of Fick's law. 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 definition of the fractional derivative operator to obtain an explicit fractional FTCS scheme for solving the fractional diffusion equation. The resulting method is amenable to a stability analysis a la von Neumann. We show that the analytical stability bounds are in excellent agreement with numerical tests. Comparison between exact analytical solutions and numerical predictions are made.
Acedo Luis
Yuste Santos B.
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