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Variational Iteration Method for Fifth-Order Boundary Value Problems Using He's Polynomials

Author

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  • Muhammad Aslam Noor
  • Syed Tauseef Mohyud-Din

Abstract

We apply the variational iteration method using He's polynomials (VIMHP) 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 Ghorbani (2007). 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.

Suggested Citation

  • Muhammad Aslam Noor & Syed Tauseef Mohyud-Din, 2008. "Variational Iteration Method for Fifth-Order Boundary Value Problems Using He's Polynomials," Mathematical Problems in Engineering, Hindawi, vol. 2008, pages 1-12, March.
    • Handle: RePEc:hin:jnlmpe:954794
    DOI: 10.1155/2008/954794
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    Cited by:

    1. Aasma Khalid & Muhammad Nawaz Naeem & Zafar Ullah & Abdul Ghaffar & Dumitru Baleanu & Kottakkaran Sooppy Nisar & Maysaa M. Al-Qurashi, 2019. "Numerical Solution of the Boundary Value Problems Arising in Magnetic Fields and Cylindrical Shells," Mathematics, MDPI, vol. 7(6), pages 1-20, June.
    2. Xin Song & Rui Wu, 2024. "An Efficient Numerical Method for Solving a Class of Nonlinear Fractional Differential Equations and Error Estimates," Mathematics, MDPI, vol. 12(12), pages 1-12, June.
    3. Nawal AL-Zaid & Amani AL-Refaidi & Huda Bakodah & Mariam AL-Mazmumy, 2022. "Solution of Second- and Higher-Order Nonlinear Two-Point Boundary-Value Problems Using Double Decomposition Method," Mathematics, MDPI, vol. 10(19), pages 1-15, September.

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