Homotopy Perturbation Method for Solving Nonlinear Differential and Integral Equations Arising in Physical Systems

Abstract

   This paper presents a rigorous and comprehensive analytical investigation of the Homotopy Perturbation Method (HPM) applied to nonlinear ordinary differential equations (ODEs), partial differential equations (PDEs) and integral equations arising in advanced physical systems Nonlinear phenomena in mathematical physics such as wave propagation and thermal distribution often lack exact closed-form solutions. HPM overcomes the limitations of traditional perturbation techniques by eliminating the need for a small parameter. In this study HPM is applied to highly nonlinear physical models including the Korteweg de Vries (KdV) equation and nonlinear heat transfer equations. The results demonstrate that HPM yields rapidly convergent analytical approximations requiring significantly less computational effort compared to alternative semi-analytical methods.