TY  - EJOU
AU  - Ju, Bingrui 
AU  - Sun, Wenxiang 
AU  - Qu, Wenzhen 
AU  - Gu, Yan 

TI  - Analysis of Extended Fisher-Kolmogorov Equation in 2D Utilizing the Generalized Finite Difference Method with Supplementary Nodes
T2  - Computer Modeling in Engineering \& Sciences

PY  - 2024
VL  - 141
IS  - 1
SN  - 1526-1506

AB  - 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.
KW  - Generalized finite difference method; nonlinear; extended Fisher-Kolmogorov equation; Crank-Nicolson scheme

DO  - 10.32604/cmes.2024.052159