Fast solution methods for space-fractional diffusion equations

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 ( N log 2 N ) . 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.

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