A new application of He's variational iteration method for quadratic Riccati differential equation by using Adomian's polynomials

In this paper, the quadratic Riccati differential equation is solved by He's variational iteration method with considering Adomian's polynomials. Comparisons were made between Adomian's decomposition method (ADM), homotopy perturbation method (HPM) and the exact solution. In this application, we do not have secular terms, and if λλ, Lagrange multiplier, is equal -1-1 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.