Summary: The quadratic Riccati differential equation is solved by J.-H. He
’s variational iteration method [Int. J. Non-Linear Mech. 34, No. 4, 699–708 (1999; Zbl 05137891
)] considering Adomian’s polynomials. Comparisons are made between the Adomian’s decomposition method, J.-H. He
’s homotopy perturbation method [Appl. Math. Comput. 151, No. 1, 287–292 (2004; Zbl 1039.65052
)] and the exact solution. In this application, we do not have secular terms, and if
, the Lagrange multiplier, is equal to
, then the Adomian’s decomposition method is obtained. The results reveal that the proposed method is very effective and simple and can be applied for other nonlinear problems.