A Second-Order Finite Difference Method for Two-Dimensional Fractional Percolation Equations

作者：Guo, Boling; Xu, Qiang^*; Zhu, Ailing

来源：Communications in Computational Physics, 2016, 19(3): 733-757.

DOI：10.4208/cicp.011214.140715a

• Fractional percolation equation
• second-order finite difference method
• Crank-Nicolson scheme
• Richardson extrapolation
• stability analysis

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.

• 出版日期2016-3
• 单位北京应用物理与计算数学研究所; 山东师范大学