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.
Keywords
- The fractional percolation equations
- Crank-Nicholson method
- ADI-CN method
- stability
- convergence
- Richardson extrapolation.
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