On the variational iteration method

In this Letter, we will consider He's variational iteration method with considering Adomian's polynomials for finding approximate and exact solutions of some nonlinear equations. Two models of interest in mathematical physics are considered and solved by means of variational iteration method. This method is based on the use of Lagrange multipliers for identification of optimal value of a parameter in a functional. This procedure is a powerful tool for solving the large amount of problems. This technique provides a sequence of functions which converges to the exact solution of the problem. Comparisons are made between standard Adomian decomposition method and the exact solutions and the proposed method. He's variational iteration method is introduced to overcome the difficulty arising in calculating Adomian polynomial in Adomian decomposition method. The results reveal that the proposed method is very effective and simple and can be applied for other nonlinear problems in mathematical physics.