TY - JOUR
T1 - A Fast Second-Order Finite Difference Method for Space-Fractional Diffusion Equations
AU - Basu , T. S.
AU - Wang , H.
JO - International Journal of Numerical Analysis and Modeling
VL - 3
SP - 658
EP - 666
PY - 2012
DA - 2012/09
SN - 9
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/652.html
KW - circulant and Toeplitz matrix, fast direct solver, fast finite difference methods, fractional diffusion equations.
AB - <p style="text-align: justify;">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.</p>