Summary: We suggest and analyze some iterative methods for solving nonlinear equations using J.-H. He’s
homotopy perturbation technique [Appl. Math. Comput. 135, No. 1, 81–84 (2003; Zbl 1023.65039
)] coupled with a system of equations. In addition, we show that the homotopy polynomial is exactly the Adomian polynomial and this establishes the equivalence between the homotopy perturbation and the decomposition techniques. Our method of establishing the equivalence between these methods is very simple as compared with others.