J. Appl. Math. & Informatics Vol. 29(2011), No. 1 - 2, pp. 381 - 394 Website: http://www.kcam.biz THE USE OF ITERATIVE METHODS FOR SOLVING NAVEIR-STOKES EQUATION SHADAN SADIGH BEHZADI * AND MOHAMMAD ALI FARIBORZI ARAGHI Abstract. In this paper, a Naveir-Stokes equation is solved by using the Adomian’s decomposition method (ADM) , modified Adomian’s decom- position method (MADM), variational iteration method (VIM), modified variational iteration method (MVIM), modified homotopy perturbation method (MHPM) and homotopy analysis method (HAM). The approxi- mate solution of this equation is calculated in the form of series which its components are computed by applying a recursive relation. The exis- tence and uniqueness of the solution and the convergence of the proposed methods are proved. A numerical example is studied to demonstrate the accuracy of the presented methods. AMS Mathematics Subject Classification : 35A15, 34A34. Key words and phrases : Naveir-Stokes equation, Adomian decomposition method , Modified Adomian decomposition method , Variational iteration method , Modified variational iteration method , Modified homotopy per- turbation method , Homotopy analysis method. 1. Introduction Naveir-Stokes equation playes an important role in mathematical physics. A lot of works have been done in order to find the numerical solution of this equa- tion. For example, finite analytic numerical solution of Naveir-Stokes equations [22], numerical solution of the Naveir-Stokes equations using variational itera- tion methods [4], numerical solution of the Naveir-Stokes equations for the flow a cylinder cascade [9], analytical solution of a time-fractional Naveir-Stokes equa- tion by Adomian decomposition method [18], using divergence free wavelets for the numerical solution of the 2-D stationary Naveir-Stokes equations [23], on the generalized Naveir-Stokes equations [6]. In this work, we develop the ADM, MADM, VIM, MVIM, MHPM and HAM to solve the Naveir-Stokes equation as follows: Received January 13, 2010. Accepted June 19, 2010. * Corresponding author. c  2011 Korean SIGCAM and KSCAM. 381