A FAST SECOND-ORDER FINITE DIFFERENCE METHOD FOR SPACE-FRACTIONAL DIFFUSION EQUATIONS.

Fractional diffusion equations provide an adequate and accurate description of transport processes that exhibit anomalous diffusion that cannot be modeled accurately by classical second-order diffusion equations. However, numerical discretizations of fractional diffusion equations yield full coefficient matrices, which require a computational operation of O(N3) per time step and a memory of O(N2) for a problem of size N. In this paper we develop a fast second-order finite difference method for space-fractional diffusion equations, which only requires memory of O(N) and computational work of O(N log2 N). Numerical experiments show the utility of the method. [ABSTRACT FROM AUTHOR]