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Zbl 1151.65334
Noor, Muhammad Aslam; Mohyud-Din, Syed Tauseef
Variational iteration method for fifth-order boundary value problems using He's polynomials. (English)
[J] Math. Probl. Eng. 2008, Article ID 954794, 12 p. (2008). ISSN 1024-123X; ISSN 1563-5147/e

Summary: We apply the variational iteration method using {\it J.-H. He}'s polynomials (VIMHP) [Phys. Scr. 76, No. 6, 680--682 (2007; Zbl 1134.34307)]'s for solving the fifth-order boundary value problems. The proposed method is an elegant combination of variational iteration and the homotopy perturbation methods and is mainly due to {\it A. Ghorbani} [``Beyond Adomian's polynomials: He's polynomials", to appear in Chaos Solitons Fractals]. The suggested algorithm is quite efficient and is practically well suited for use in these problems. The proposed iterative scheme finds the solution without any discritization, linearization, or restrictive assumptions. Several examples are given to verify the reliability and efficiency of the method. The fact that the proposed technique solves nonlinear problems without using Adomian's polynomials can be considered as a clear advantage of this algorithm over the decomposition method.

MSC 2000:: *65L10 Boundary value problems for ODE (numerical methods)

Citations: Zbl 1134.34307

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