[1]陈心妍,张馨心,蔡耀雄.非局部Gray-Scott模型的二阶线性化差分格式[J].华侨大学学报(自然科学版),2024,45(4):524-533.[doi:10.11830/ISSN.1000-5013.202307024]
　CHEN Xinyan,ZHANG Xinxin,CAI Yaoxiong.Second-Order Linearized Difference Scheme for Nonlocal Gray-Scott Model[J].Journal of Huaqiao University(Natural Science),2024,45(4):524-533.[doi:10.11830/ISSN.1000-5013.202307024]
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非局部Gray-Scott模型的二阶线性化差分格式()
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《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第45卷
期数:
2024年第4期
页码:
524-533
栏目:
出版日期:
2024-07-20

文章信息/Info

Title:
Second-Order Linearized Difference Scheme for Nonlocal Gray-Scott Model
文章编号:
1000-5013(2024)04-0524-10
作者:
陈心妍;  张馨心;  蔡耀雄
华侨大学 数学科学学院, 福建 泉州 362021
Author(s):
CHEN Xinyan;  ZHANG Xinxin;  CAI Yaoxiong
School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China
关键词:
非局部Gray-Scott模型;  算子分裂;  稳定性;  有效性
Keywords:
nonlocal Gray-Scott model;  operator splitting;  stability;  effectiveness
分类号:
O241.8
DOI:
10.11830/ISSN.1000-5013.202307024
文献标志码:
A
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。
Abstract:
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.

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备注/Memo

备注/Memo:
收稿日期: 2023-07-22
通信作者: 蔡耀雄(1979-),男,讲师,主要从事偏微分方程数值解及理论的研究。E-mail:cai_yx@126.com。
基金项目: 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)
更新日期/Last Update: 2024-07-20