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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 {\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.

65L05Initial value problems for ODE (numerical methods)
34A34Nonlinear ODE and systems, general
Full Text: DOI
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