Second-order accurate numerical approximations for the fractional percolation equations


Authors

Xiucao Yin - Department of Mathematics, South China Agricultural University, Guangzhou 510640, P. R. China.
Lang Li - Department of Mathematics, South China Agricultural University, Guangzhou 510640, P. R. China.
Shaomei Fang - Department of Mathematics, South China Agricultural University, Guangzhou 510640, P. R. China.


Abstract

First, we examine a practical numerical method which based on the classical Crank-Nicholson (CN) method combined with Richardson extrapolation is used to solve a class of one-dimensional initial-boundary value fractional percolation equation (FPE) with variable coefficients on a finite domain. Secondly, we present ADI-CN method for the two-dimensional fractional percolation equation. Stability and convergence of these methods are proved. Using these methods, we can achieve second-order convergence in time and space. Finally, numerical examples are presented to verify the order of convergence.


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