A Second-Order Finite Difference Method for Two-Dimensional Fractional Percolation Equations (Communications in Computational Physics, 2018)
A finite difference method which is second-order accurate in time and inspace is proposed for two-dimensional fractional percolation equations. Using theFourier transform, a general approximation for the mixed fractional derivatives is analyzed.An approach based on the classical Crank-Nicolson scheme combined withthe Richardson extrapolation is used to obtain temporally and spatially second-orderaccurate numerical estimates. Consistency, stability and convergence of the methodare established. Numerical experiments illustrating the effectiveness of the theoreticalanalysis are provided.