Volume 19, Issue 3
A Second-Order Finite Difference Method for Two-Dimensional Fractional Percolation Equations

Boling Guo, Qiang Xu & Ailing Zhu

Commun. Comput. Phys., 19 (2016), pp. 733-757.

Published online: 2018-04

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  • Abstract

A finite difference method which is second-order accurate in time and in space is proposed for two-dimensional fractional percolation equations. Using the Fourier transform, a general approximation for the mixed fractional derivatives is analyzed. An approach based on the classical Crank-Nicolson scheme combined with the Richardson extrapolation is used to obtain temporally and spatially second-order accurate numerical estimates. Consistency, stability and convergence of the method are established. Numerical experiments illustrating the effectiveness of the theoretical analysis are provided.

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