@Article{IJNAM-9-658,
author = {Basu , T. S. and Wang , H.},
title = {A Fast Second-Order Finite Difference Method for Space-Fractional Diffusion Equations},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2012},
volume = {9},
number = {3},
pages = {658--666},
abstract = {<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>},
issn = {2617-8710},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/ijnam/652.html}
}