Journal Article

A Method of Lines Scheme with Third-Order Finite Differences for Burgers–Huxley Equation

Yaseen, Muhammad, Mohammed, Naglaa, Hamza, Muhammad Ameer, Mohamed, Khidir Shaib

2026

Overview

The Burgers–Huxley equation is a nonlinear partial differential equation that incorporates convective, diffusive and reactive effects and arises in various reaction–diffusion and fluid flow models. In this paper, a numerical method based on the method of lines is proposed for its solution. The spatial derivatives are approximated using a third-order finite difference scheme, which converts the governing partial differential equation into a system of ordinary differential equations. The resulting semi-discrete system is solved in time using the classical fourth-order Runge–Kutta method. The stability and convergence properties of the proposed scheme are analyzed to establish its numerical reliability. Several numerical experiments are presented to illustrate the accuracy and efficiency of the method. The computed results confirm that the proposed approach provides accurate and stable solutions for the Burgers–Huxley equation.

• Publisher: MDPI AG
• Subject: Accuracy / Approximation / Boundary conditions / Burgers–Huxley equation / convergence analysis / Discrete systems / Finite difference method / Fluid flow / Mathematical analysis / Method of lines / Methods / Neural networks / Nonlinear differential equations / nonlinear system / Numerical analysis / Numerical methods / Partial differential equations / Propagation / Runge-Kutta method / stability analysis / third-order finite differences