Open Access

ARTICLE

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

by Bingrui Ju^1,2, Wenxiang Sun², Wenzhen Qu^1,2,*, Yan Gu²

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

* Corresponding Author: Wenzhen Qu. Email:

(This article belongs to the Special Issue: New Trends on Meshless Method and Numerical Analysis)

Computer Modeling in Engineering & Sciences 2024, 141(1), 267-280. https://doi.org/10.32604/cmes.2024.052159

Received 25 March 2024; Accepted 28 June 2024; Issue published 20 August 2024

Abstract

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.

---

Keywords

---