On the Exact Solution of Burgers-Huxley Equation Using the Homotopy Perturbation Method

TL;DR

This paper demonstrates that the Homotopy Perturbation Method (HPM) efficiently and accurately finds exact solutions to the nonlinear Burgers-Huxley equations through three case studies, confirming its effectiveness.

Contribution

The paper applies HPM to solve Burgers-Huxley equations and proves its rapid convergence and accuracy in obtaining exact solutions for nonlinear differential equations.

Findings

HPM converges rapidly to exact solutions

HPM provides acceptable accuracy for Burgers-Huxley equations

HPM is an efficient algorithm for nonlinear differential equations

Abstract

The Homotopy Perturbation Method (HPM) is used to solve the Burgers-Huxley non-linear differential equations. Three case study problems of Burgers-Huxley are solved using the HPM and the exact solutions are obtained. The rapid convergence towards the exact solutions of HPM is numerically shown. Results show that the HPM is efficient method with acceptable accuracy to solve the Burgers-Huxley equation. Also, the results prove that the method is an efficient and powerful algorithm to construct the exact solution of non-linear differential equations.