Second-order accurate numerical approximations for the fractional percolation equations

The Journal of Nonlinear Sciences and its Applications

Shaomei Fang¹  Lang Li¹  Xiucao Yin¹ 

[1] Department of Mathematics, South China Agricultural University, Guangzhou 510640, P. R. China.

关键词: The fractional percolation equations;    Crank-Nicholson method;    ADI-CN method;    stability;    convergence;    Richardson extrapolation.;   

DOI  :  10.22436/jnsa.010.08.08

学科分类：社会科学、人文和艺术（综合）

来源: Shomal University

【 摘 要 】

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.

【 授权许可】

Unknown