Several new iterative methods for solving nonlinear algebraic equations incorporating homotopy perturbation method (HPM)

Abstract

In this paper, several new iterative methods for solving nonlinear algebraic equations are presented. The iterative formulas are based on the He's homotopy perturbation method (HPM). It is shown that the new methods lead to eight algorithms which are of fifth, seventh, tenth and fourteenth order convergence. These methods result in real or complex simple roots of certain nonlinear equations. The merit of the new algorithms is that, in case the nonlinear equation have complex roots, it can give complex solutions even when the initial approximation is chosen real. Several examples are presented and compared to other methods, showing the accuracy and fast convergence of the presented method. Key words: Iterative methods, homotopy perturbation method, nonlinear algebraic equations, efficency index, convergence order.