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Variational Iteration Method for Initial and Boundary Value Problems Using He's Polynomials

Author

Listed:
  • Syed Tauseef Mohyud-Din
  • Ahmet Yildirim
  • M. M. Hosseini

Abstract

This paper outlines a detailed study of the coupling of He's polynomials with correction functional of variational iteration method (VIM) for solving various initial and boundary value problems. The elegant coupling gives rise to the modified versions of VIM which is very efficient in solving nonlinear problems of diversified nature. It is observed that the variational iteration method using He's polynomials (VIMHP) is very efficient, easier to implements, and more user friendly. Several examples are given to reconfirm the efficiency of the proposed VIMHP.

Suggested Citation

  • Syed Tauseef Mohyud-Din & Ahmet Yildirim & M. M. Hosseini, 2010. "Variational Iteration Method for Initial and Boundary Value Problems Using He's Polynomials," International Journal of Differential Equations, Hindawi, vol. 2010, pages 1-28, April.
    • Handle: RePEc:hin:jnijde:426213
    DOI: 10.1155/2010/426213
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    Cited by:

    1. Abdon Atangana & Adem Kılıçman, 2013. "Analytical Solutions of Boundary Values Problem of 2D and 3D Poisson and Biharmonic Equations by Homotopy Decomposition Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. Din Prathumwan & Inthira Chaiya & Kamonchat Trachoo, 2025. "Analytical Solutions of Heat‐Like Equation Using Elzaki Transform Variational Iteration Method: Black–Scholes Equation," Complexity, John Wiley & Sons, vol. 2025(1).
    3. Yanqin Liu, 2012. "Variational Homotopy Perturbation Method for Solving Fractional Initial Boundary Value Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    4. Rabab Alyusof & Shams Alyusof & Naveed Iqbal & Mohammad Asif Arefin, 2022. "Novel Evaluation of the Fractional Acoustic Wave Model with the Exponential‐Decay Kernel," Complexity, John Wiley & Sons, vol. 2022(1).

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