Improvement of the homotopy perturbation method to nonlinear problems

Abstract

This paper proposes an effective improvement of the homotopy perturbation method (HPM) by using Jacobi and He's polynomials to solve some nonlinear ordinary differential equations. With this method, the source terms of ordinary differential equations can be expanded in series of shifted Jacobi polynomials. Numerical results are given in this paper to illustrate the reliability of this method with nonlinear ordinary differential equations.