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Zbl 1194.65101
Mohyud-Din, Syed Tauseef; Yildirim, Ahmet
Solutions of tenth and ninth-order boundary value problems by modified variational iteration method. (English)
[J] Appl. Appl. Math. 5, No. 1, 11-25, electronic only (2010). ISSN 1932-9466/e

Summary: We apply the modified variational iteration method (MVIM) for solving the ninth and tenth-order boundary value problems. The proposed modification is made by introducing He's polynomials in the correction functional. 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 discretization, 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 the Adomian's polynomials can be considered as a clear advantage of this algorithm over the decomposition method.

MSC 2000:: *65L99 Numerical methods for ODE

Keywords: modified variational iteration method; He's polynomials; nonlinear problems; initial value problems; boundary value problems; error estimates

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Zentralblatt MATH Berlin [Germany]