Second-order accurate numerical approximations for the fractional percolation equations

Volume 10, Issue 8, pp 4122--4136

Publication Date: 2017-08-09

http://dx.doi.org/10.22436/jnsa.010.08.08

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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