非局部Gray-Scott模型的二阶线性化差分格式  

Second-Order Linearized Difference Scheme for Nonlocal Gray-Scott Model

作　　者：陈心妍 张馨心 蔡耀雄 CHEN Xinyan;ZHANG Xinxin;CAI Yaoxiong(School of Mathematical Sciences,Huaqiao University,Quanzhou 362021,China)

机构地区：[1]华侨大学数学科学学院,福建泉州362021

出　　处：《华侨大学学报（自然科学版）》2024年第4期524-533,共10页Journal of Huaqiao University(Natural Science)

基　　金：国家自然科学基金资助项目(11701196);福建省自然科学基金资助项目(2020J01074,2021J01306)。

摘　　要：研究周期边界条件下的非局部Gray-Scott模型,提出一种高效数值格式。基于算子分裂思想将原问题拆分为线性非局部子问题和非线性子问题。对于线性非局部子问题,结合复化梯形公式和Crank-Nicolson公式,建立时空二阶差分格式;对于非线性子问题,结合Crank-Nicolson公式及Rubin-Graves线性化技术,建立线性求解格式。结果表明:非局部Gray-Scott模型的二阶线性化差分格式具有稳定性、收敛性及有效性。An efficient numerical scheme is proposed by studying the nonlocal Gray-Scott model under periodic boundary conditions.Based on the idea of operator splitting,the original problem is divided into a linear nonlocal subproblem and a nonlinear subproblem.To linear nonlocal subproblem,a spatiotemporal second-order difference scheme is established by combining the complex trapezoidal formula and Crank Nicholson formula.To nonlinear subproblem,a linear solution format is established by combining Crank Nicholson formula and Rubin Graves linearization technique.The results show that the second-order linearized difference scheme of the nonlocal Gray-Scott model is stable,convergent and efficient.

关 键 词：非局部Gray-Scott模型 算子分裂 稳定性 有效性 

分 类 号：O241.8[理学—计算数学]