The Journal of Nonlinear Sciences and its Applications | |
Second-order accurate numerical approximations for the fractional percolation equations | |
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
【 预 览 】
Files | Size | Format | View |
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RO201902018567748ZK.pdf | 737KB | download |