Variational iteration method for fifth-order boundary value problems using He’s polynomials.

*(English)*Zbl 1151.65334Summary: We apply the variational iteration method using 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 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:

65L10 | Numerical solution of boundary value problems involving ordinary differential equations |

##### Citations:

Zbl 1134.34307
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\textit{M. A. Noor} and \textit{S. T. Mohyud-Din}, Math. Probl. Eng. 2008, Article ID 954794, 12 p. (2008; Zbl 1151.65334)

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