Fast solution methods for space-fractional diffusion equations

Authors:
Hong Wang;Ning Du
Affiliations:
-;-
Venue:
Journal of Computational and Applied Mathematics
Year:
2014

Citing 6
Cited 1

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Abstract

We develop fast solution methods for a shifted Grunwald finite difference method for steady-state and time-dependent space-fractional diffusion equations. These methods reduce the memory requirement of the finite difference scheme from O(N^2) to O(N) and the computational complexity from O(N^3) to O(Nlog^2N). Preliminary numerical example runs show the utility of these methods over the traditional direct solvers of the finite difference methods, in terms of computational cost and memory requirements.