A fast high-order compact difference method for the fractal mobile/immobile transport equation

Abstract

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.