[1]张馨心,陈心妍,蔡耀雄.Gray-Scott模型的高阶紧致线性化差分格式[J].华侨大学学报(自然科学版),2025,46(3):347-355.[doi:10.11830/ISSN.1000-5013.202404026]
　ZHANG Xinxin,CHEN Xinyan,CAI Yaoxiong.High-Order Compact Linearized Difference Scheme for Gray-Scott Model[J].Journal of Huaqiao University(Natural Science),2025,46(3):347-355.[doi:10.11830/ISSN.1000-5013.202404026]
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Gray-Scott模型的高阶紧致线性化差分格式()
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《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第46卷
期数:
2025年第3期
页码:
347-355
栏目:
出版日期:
2025-05-20

文章信息/Info

Title:
High-Order Compact Linearized Difference Scheme for Gray-Scott Model
文章编号:
1000-5013(2025)03-0347-09
作者:
张馨心;  陈心妍;  蔡耀雄
华侨大学 数学科学学院, 福建 泉州 362021
Author(s):
ZHANG Xinxin;  CHEN Xinyan;  CAI Yaoxiong
School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China
关键词:
Gray-Scott 方程;  算子分裂;  4阶紧致差分格式;  Rubin-Graves 线性化技术;  稳定性;  有效性
Keywords:
Gray-Scott equation;  operator splitting;  fourth-order compact difference scheme;  Rubin-Graves linearization technique;  stability;  validity
分类号:
O241.8
DOI:
10.11830/ISSN.1000-5013.202404026
文献标志码:
A
摘要:
研究Dirichlet边界条件下的整数阶Gray-Scott方程。考虑将紧差分方法与算子分裂算法相结合,提出一种高效求解Gray-Scott方程的数值格式。首先,基于算子分裂思想将原问题分解为线性部分与非线性部分;然后,线性子问题采用4阶紧致差分格式,非线性子问题采用Crank-Nicolson差分格式,并且利用Rubin-Graves线性化技术处理非线性项,建立线性求解格式,实现有效求解;最后,严格证明了格式的稳定性,给出其误差估计,并且通过数值实验验证了格式的有效性。
Abstract:
The Gray-Scott equation of integer order with Dirichlet boundary condition is studied. We propose a numerical scheme for solving efficiently the Gray-Scott equation by combining the compact difference method and the operator splitting algorithm. Firstly, the original problem is decomposed into linear and nonlinear parts based on the operator splitting idea. Then the linear subproblem is solved by using the fourth-order compact difference scheme, the nonlinear subproblem is solved by using the Crank-Nicolson difference scheme, and the nonlinear terms are handled by using the Rubin-Graves linearization technique to build a linear solving format to achieve an efficient solution. Finally, the stability of the scheme is proved, the error estimate of given, and the validity of the scheme is verified by numerical experiments.

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备注/Memo

备注/Memo:
收稿日期: 2024-04-10
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: 福建省自然科学基金资助项目(2020J01074)
更新日期/Last Update: 2025-05-20