空间分数阶Gray-Scott方程的数值算法  

Numerical Algorithm for the Gray-Scott Equation of Spatial Fractional Order

作　　者：刘将华 谢彩云 郑子晴 

机构地区：[1]华侨大学数学科学学院,福建 泉州

出　　处：《应用数学进展》2023年第3期1120-1129,共10页Advances in Applied Mathematics

摘　　要：本文基于算子分裂方法,提出了求解分数阶Gray-Scott模型的一种高效数值逼近格式。首先采用算子分裂法将原问题分解为线性子问题和非线性子问题:线性子问题采用Crank-Nicolson(CN)格式结合二阶中心差分,建立整体二阶的数值计算格式;非线性子问题采用CN格式结合Rubin-Graves线性化技术,建立线性化求解格式;并给出算法的稳定性和收敛性分析。最后,通过数值算例验证了算法的有效性。In this paper, an efficient numerical approximation algorithm for solving the fractional-order Gray-Scott model is proposed based on the operator splitting method. Firstly, the operator splitting method is used to decompose the original problem into linear and nonlinear subproblems: the lin-ear subproblem adopts the Crank-Nicolson (CN) format combined with the second-order central difference to establish the overall second-order numerical computation format;the nonlinear sub-problem adopts the CN format combined with the Rubin-Graves linearization technique to establish the linearized solution format;and the stability and convergence analysis of the algorithm are given. Finally, the validity of the algorithm is verified by numerical examples.

关 键 词：空间分数阶Gray-Scott方程 算子分裂 差分方法 Rubin-Graves线性化技术 

分 类 号：O17[理学—数学]