Geodesic
Second-order accurate numerical approximations for the fractional percolation equations
Yin, Xiucao1 ; Li, Lang1 ; Fang, Shaomei1
1 Department of Mathematics, South China Agricultural University, Guangzhou 510640, P. R. China
Journal of nonlinear sciences and its applications, Tome 10 (2017) no. 8, p. 4122-4136.

Voir la notice de l'article provenant de la source International Scientific Research Publications

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.
DOI : 10.22436/jnsa.010.08.08
Classification : 65M06, 65M12
Keywords: The fractional percolation equations, Crank-Nicholson method, ADI-CN method, stability, convergence, Richardson extrapolation.

Yin, Xiucao 1 ; Li, Lang 1 ; Fang, Shaomei 1

1 Department of Mathematics, South China Agricultural University, Guangzhou 510640, P. R. China 
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Yin, Xiucao; Li, Lang; Fang, Shaomei. Second-order accurate numerical approximations for the fractional percolation equations. Journal of nonlinear sciences and its applications, Tome 10 (2017) no. 8, p. 4122-4136. doi : 10.22436/jnsa.010.08.08. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.010.08.08/

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