On numerical solutions of one-dimensional nonlinear Burgers' equation and convergence of the decomposition method

In this paper, the one-dimensional nonlinear Burgers' equation is solved by using the Adomian decomposition method (ADM). We prove the convergence of this method applied to the nonlinear Burgers' equation. The approximate solution of this equation is calculated in the form of a series with easily computable components. The accuracy of the proposed numerical scheme is examined by comparison with other analytical and numerical results. In addition, the numerical results shows that our present method is more easy and accurate than other methods. The method performs well.