A comparison between Adomian's polynomials and He's polynomials for nonlinear functional equations (Q474298)

Summary: We will compare the standard Adomian decomposition method and the homotopy perturbation method applied to obtain the solution of nonlinear functional equations. We prove analytically that the two methods are equivalent for solving nonlinear functional equations. \textit{A. Ghorbani} [Chaos Solitons Fractals 39, No. 3, 1486--1492 (2009; Zbl 1197.65061)] presented a new definition which he called as He's polynomials. In this paper, we also show that He's polynomials are only the Adomian polynomials.