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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 1342.34005)] 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.

65L05 Numerical methods for initial value problems involving ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
Full Text: DOI
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