ABSTRACT
In this paper, we present a high-order compact finite difference scheme for fractal mobile/immobile transport model with a Caputo fractional time derivative. The compact finite difference scheme is stable and convergent with convergence order in -norm. Furthermore, because of the non-local property of fractional differential operators, it is necessary to find a fast technique to reduce the computational cost. We develop a fast solution technique which is based on a fast Fourier transform. The computational work will reduce to while the direct method requires the computational cost of , where and τ is the size of time step, and h is the size of space step. Moreover, numerical results are consistent with the theoretical analysis.
Acknowledgments
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Disclosure statement
No potential conflict of interest was reported by the authors.