Homotopy Perturbation Method and the Korteweg-de Vries Equation

Abstract

In this research project paper, our main aim is to solve linear and non-linear di_erential equations by perturbation methods. This study include the following aspects: (1) Give some basic concepts of the regular, singular and homotopy perturbation method. (2) Use the regular, singular and homotopy perturbation method to solve ordinary di_erential equations and partial di_erential equations. (3) Describe the interesting concept of shallow water waves and derive the Korteweg-de Vries equation. (4) Use homotopy perturbation method to solve the Korteweg-de Vries equation