European Scientific Journal April 2013 edition vol.9, No.12 ISSN: 1857 – 7881 (Print) e - ISSN 1857- 7431 202 EXTENSION OF HOMOTOPY PERTURBATION METHOD FOR SOLVING NONLINEAR SYSTEMS Mustafa.Q. Khirallah Department of Mathematics and Computer Science, Faculty of Science, Ibb University, Yemen M.A. Hafiz Department of mathematics, Faculty of Science and arts, Najran University, Saudi Arabia Abstract In this paper, a homotopy perturbation method (HPM) is extended and applied for solving system of nonlinear equations of n-dimensional with n-variables. Also, numerical examples are used to show the performance of the presented method, on a series of examples published in the literature, and to compare with other literature methods. Keywords: Homotopy method, perturbation method, System of nonlinear equations, Iterative method, Newton's method Introduction Homotopy perturbation methods HPM play a very important role in solving several mathematical problems such as linear and nonlinear system equations, differential equation and integral equations (He, 2000-2006; Soltanian, 2010; Dehghan, 2008-2011 ). The basic idea of HPM is to simplify the difficult equation systems by converting them into either linear or nonlinear system equations so that they can be solved. In the recent years, HPM attracts the attention of the authors, because solutions of this method offer a high degree of accuracy and convergence (El-Shahed, 2005; Ghasemi, 2006; Javidi, 2007; Abbasbandy2003). H. He (He; 2005) suggested an iterative method for solving the nonlinear equations by rewriting the given nonlinear equation as a system of coupled equations. This technique has been used by Chun (Chun2005) and Noor et. al. (Noor et.al,2006-2007) to suggest some higher order convergent iterative methods for solving nonlinear equations. In 2007, A. Golbabai et.al(Golbabai et.al,2007) applied HPM for solving system of nonlinear equations