A COMPARATIVE STUDY OF STENCIL-BASED METHOD OF LINES FOR SOLVING THE BURGERS-HUXLEY EQUATION

Abstract

This study presents a numerical investigation of the Burgers-Huxley equation using the Method of Lines (MoL) with varying stencil points.The Burgers-Huxley equation models complex nonlinear phenomena involving reaction, diffusion, and convection processes and is prominent in biological and physical sciences.Spatial discretization was performed using central finite difference schemes with three, five, seven, nine, and eleven-point stencils to analyze their impact on solution accuracy and convergence.The resulting system of ordinary differential equations was solved using standard time integration methods.Comparative analysis across different stencil sizes and simulation times shows that higher-order stencils significantly reduce the approximation error, with the seven-point stencil offering an optimal balance between computational efficiency and accuracy.Notably, the method achieved an absolute error as low as 7.63 10 -10 at x = 5.0 and T = 15 using the seven-point stencil.The findings highlight the MoL's robustness and offer guidance on stencil selection for accurate and efficient modeling of nonlinear partial differential equations.