j Izadian - Department of Mathematics, Faculty of Sciences, Mashhad Branch, Islamic Azad Univer-sity, Mashhad, Iran.
r Abrishami - Department of Mathematics, Faculty of Sciences, Mashhad Branch, Islamic Azad Univer-sity, Mashhad, Iran
m jalili - Department of Mathematics, Neyshabur Branch, Islamic Azad University, Neyshabur,Iran.

A new approach utilizing Newton Method and Homotopy Analysis Method (HAM) is proposed for solving nonlinear system of equations. Accelerating the rate of convergence of HAM, and obtaining a global quadratic rate of convergence are the main purposes of this approach. The numerical results demonstrate the efficiency and the performance of proposed approach. The comparison with conventional homotopy method, Newton Method and HAM shows the great freedom of selecting the initial guess, in this approach.

Homotopy Analysis Method; Zero order deformation equations; Control convergence parameter; Newton s method; Iterative method; Multistep iterative method; Order of convergence