一类二维常系数反应扩散方程的交替方向隐式差分方法  

Study on the Alternating Direction Implicit Difference Method for a Class of Two-Dimensional Constant Coefficient Reaction-Diffusion Equations

作　　者：刘天源 张海湘 杨雪花 刘嘉 张伟燕 LIU Tianyuan;ZHANG Haixiang;YANG Xuehua;LIU Jia;ZHANG Weiyan(College of Science,Hunan University of Technology,Zhuzhou Hunan 412007,China)

机构地区：[1]湖南工业大学理学院,湖南株洲412007

出　　处：《湖南工业大学学报》2025年第4期96-104,共9页Journal of Hunan University of Technology

基　　金：国家自然科学基金资助项目(12226340,12226337,12126321);湖南省自然科学基金资助项目(2024JJ7146,2022JJ50083);湖南省教育厅优秀青年基金资助项目(21B0550)。

摘　　要：对一类二维常系数反应扩散方程,建立了P-R交替方向隐格式和D’Yakonov交替方向隐格式这两类交替方向隐式差分格式,并应用能量分析法证明了差分格式解的存在性,稳定性及收敛性。最后,通过两个数值算例验证了理论结果。In view of a class of two-dimensional constant coefficient reaction-diffusion equations,two types of alternating direction implicit difference schemes have thus been established:P-R alternating direction implicit scheme and D’Yakonov alternating direction implicit scheme.By adopting energy analysis method,the existence,stability,and convergence of the difference scheme solutions can be proved.Finally,the theoretical results are verified by two numerical examples.

关 键 词：计算数学 反应扩散方程 有限差分格式 能量分析法 交替方向隐格式 

分 类 号：O241.82[理学—计算数学]