A fourth-order compact ADI scheme for two-dimensional Riesz space fractional nonlinear reaction-diffusion equation
A fourth-order compact ADI scheme for two-dimensional Riesz space fractional nonlinear reaction-diffusion equation
复制标题
二维Riesz空间分数阶非线性反应扩散方程的四阶紧致ADI格式
DOI：
10.1080/00207160.2019.1671587
复制
发表时间：
2019
影响因子：
1.8
通讯作者：
Cao Xuenian
中科院分区：
文献类型：
--
作者：
Hu Dongdong;Cao Xuenian
本文给出了一个二阶向后差分公式（简称：二阶向后差分公式）。BDF 2）逼近一阶时间偏导数，Riesz分数阶导数用四阶紧算子逼近，构造了一类新的交替方向隐式差分格式（简称AID2）。ADI）构造了二维Riesz空间分数阶非线性反应扩散方程。数值方法的稳定性和收敛性进行了分析。数值实验表明该方法是有效的。
In this paper, a second-order backward difference formula (abbr. BDF2) is used to approximate first-order time partial derivative, the Riesz fractional derivatives are approximated by fourth-order compact operators, a class of new alternating-direction implicit difference scheme (abbr. ADI) is constructed for two-dimensional Riesz space fractional nonlinear reaction–diffusion equation. Stability and convergence of the numerical method are analysed. Numerical experiments demonstrate that the proposed method is effective.