Abstract
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.
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