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

作者：Basu Treena S^*; Wang Hong

来源：International Journal of Numerical Analysis and Modeling, 2012, 9(3): 658-666.

• circulant and Toeplitz matrix
• fast direct solver
• fast finite difference methods
• 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(N-3) per time step and a memory of O(N-2) 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 log(2) N). Numerical experiments show the utility of the method.

• 出版日期2012