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Zbl 1120.65083
Abbasbandy, S.
A new application of He's variational iteration method for quadratic Riccati differential equation by using Adomian's polynomials. (English)
[J] J. Comput. Appl. Math. 207, No. 1, 59-63 (2007). ISSN 0377-0427

Summary: The quadratic Riccati differential equation is solved by {\it 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, {\it 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 2000:: *65L05 Initial value problems for ODE (numerical methods)
34A34 Nonlinear ODE and systems, general

Keywords: variational iteration method; Adomian decomposition method; homotopy perturbation method; comparison of methods; quadratic Riccati differential equation

Citations: Zbl 05137891; Zbl 1039.65052

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