A new application of Heʹs variational iteration method for quadratic Riccati differential equation by using Adomianʹs polynomials

In this paper, the quadratic Riccati differential equation is solved by Heʹs variational iteration method with considering Adomianʹs polynomials. Comparisons were made between Adomianʹs decomposition method (ADM), homotopy perturbation method (HPM) and the exact solution. In this application, we do not have secular terms, and if λ , Lagrange multiplier, is equal - 1 then the Adomianʹs decomposition method is obtained. The results reveal that the proposed method is very effective and simple and can be applied for other nonlinear problems.