fa عمومى General پژوهشي Research In this paper, a regularized long-wave equation (RLWE) is solved by using the Adomian's decomposition method (ADM) , modified Adomian's decomposition method (MADM), variational iteration method (VIM), modified variational iteration method (MVIM) and homotopy analysis method (HAM). The approximate solution of this equation is calculated in the form of series which its components are computed by applying a recursive relation. The existence 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. Regularized long-wave equation, Adomian decomposition method , Modified Adomian decomposition method , Variational iteration method , Modified variational iteration method , Homotopy analysis method. 55 68 http://ijorlu.lahijan.iau.ir/browse.php?a_code=A-10-298-2&slc_lang=fa&sid=1 T. Allahviranloo allahviranloo@yahoo.com 1003194753284600901 1003194753284600901 Yes Department of Mathematics, Islamic Azad University, Parand Branch, Parand Sh. Sadigh Behzadi shadan_behzadi@yahoo.com 1003194753284600902 1003194753284600902 No Department of Mathematics,Islamic Azad University,Qazvin Branch,Qazvin