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A new application of He’s variational iteration method for quadratic Riccati differential equation by using Adomian’s polynomials. (English) Zbl 1120.65083
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 $\lambda$ , the Lagrange multiplier, is equal to $-1$, 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.
##### MSC:
 65L05 Initial value problems for ODE (numerical methods) 34A34 Nonlinear ODE and systems, general