TY - JOUR
T1 - A Second-Order Finite Difference Method for Two-Dimensional Fractional Percolation Equations
JO - Communications in Computational Physics
VL - 3
SP - 733
EP - 757
PY - 2018
DA - 2018/04
SN - 19
DO - http://doi.org/10.4208/cicp.011214.140715a
UR - https://global-sci.org/intro/article_detail/cicp/11107.html
KW - 
AB - <p style="text-align: justify;">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.</p>