Analysis of Extended Fisher-Kolmogorov Equation in 2D Utilizing the Generalized Finite Difference Method with Supplementary Nodes  

作　　者：Bingrui Ju Wenxiang Sun Wenzhen Qu Yan Gu 

机构地区：[1]Key Laboratory of Road Construction Technology and Equipment of MOE,Chang’an University,Xi’an,710018,China [2]School of Mathematics and Statistics,Qingdao University,Qingdao,266071,China

出　　处：《Computer Modeling in Engineering & Sciences》2024年第10期267-280,共14页工程与科学中的计算机建模（英文）

基　　金：supported by the Key Laboratory of Road Construction Technology and Equipment(Chang’an University,No.300102253502);the Natural Science Foundation of Shandong Province of China(GrantNo.ZR2022YQ06);the Development Plan of Youth Innovation Team in Colleges and Universities of Shandong Province(Grant No.2022KJ140).

摘　　要：In this study,we propose an efficient numerical framework to attain the solution of the extended Fisher-Kolmogorov(EFK)problem.The temporal derivative in the EFK equation is approximated by utilizing the Crank-Nicolson scheme.Following temporal discretization,the generalized finite difference method(GFDM)with supplementary nodes is utilized to address the nonlinear boundary value problems at each time node.These supplementary nodes are distributed along the boundary to match the number of boundary nodes.By incorporating supplementary nodes,the resulting nonlinear algebraic equations can effectively satisfy the governing equation and boundary conditions of the EFK equation.To demonstrate the efficacy of our approach,we present three numerical examples showcasing its performance in solving this nonlinear problem.

关 键 词：Generalized finite difference method nonlinear extended Fisher-Kolmogorov equation Crank-Nicolson scheme 

分 类 号：O17[理学—数学]