On systems of nonlinear equations: some modified iteration formulas by the homotopy perturbation method with accelerated fourth- and fifth-order convergence

This paper is concerned with the development of efficient algorithms for solving the system of nonlinear equations based on the modified homotopy perturbation method. The analysis of convergence shows that the proposed methods are fourth and fifth-order convergence. Several numerical examples are presented. Comparisons are made to confirm the reliability and effectiveness of the proposed schemes.