A Second-Order Finite Difference Method for Two-Dimensional Fractional Percolation Equations. (16th March 2016) - Guo, Boling; Xu, Qiang; Zhu, Ailing
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.