Second-order accurate numerical approximations for the fractional percolation equations

Volume 10, Issue 8, pp 4122--4136 http://dx.doi.org/10.22436/jnsa.010.08.08

Publication Date: August 09, 2017 Submission Date: July 06, 2016

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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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Keywords

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

MSC

•  65M06
•  65M12

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