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
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。
Abstract: 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.
文章引用：刘将华, 谢彩云, 郑子晴. 空间分数阶Gray-Scott方程的数值算法[J]. 应用数学进展, 2023, 12(3): 1120-1129. https://doi.org/10.12677/AAM.2023.123114

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