In this article, a novel meshless local collocation method is proposed for the numerical solution of the three-dimensional (3D) extended Fisher–Kolmogorov (EFK) equation. The second-order Crank–Nicolson scheme and the meshless generalized finite difference method (GFDM) are respectively adopted to discretize the time and spatial derivatives of the EFK equation. A different setting of collocation nodes is introduced to the meshless GFDM for solving the nonlinear fourth order system resulting after the time discretization process. Two numerical experiments are carried out to verify the accuracy and the convergence of the developed numerical meshless algorithm.

本文针对三维（3D）扩展Fisher-Kolmogorov（EFK）方程的数值解提出了一种新的无网格局部配置方法。分别采用二阶 Crank-Nicolson 格式和无网格广义有限差分法 (GFDM) 对 EFK 方程的时间和空间导数进行离散化。在无网格 GFDM 中引入了不同的配置节点设置，用于求解时间离散化过程后产生的非线性四阶系统。进行了两次数值实验来验证所开发的数值无网格算法的准确性和收敛性。