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

Boling Guo ,  Qiang Xu and Ailing Zhu

10.4208/cicp.011214.140715a

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

Preview Full PDF BiBTex 94 394
  • 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.

  • History

Published online: 2018-04

  • Keywords

  • AMS Subject Headings

  • Cited by