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A New Variational Iteration Method for a Class of Fractional Convection-Diffusion Equations in Large Domains

Author

Listed:
  • Mohammad Abolhasani

    (Department of Mathematics, Science and Research Branch, Islamic Azad university, Tehran 14778, Iran)

  • Saeid Abbasbandy

    (Department of Mathematics, Science and Research Branch, Islamic Azad university, Tehran 14778, Iran)

  • Tofigh Allahviranloo

    (Department of Mathematics, Science and Research Branch, Islamic Azad university, Tehran 14778, Iran)

Abstract

In this paper, we introduced a new generalization method to solve fractional convection–diffusion equations based on the well-known variational iteration method (VIM) improved by an auxiliary parameter. The suggested method was highly effective in controlling the convergence region of the approximate solution. By solving some fractional convection–diffusion equations with a propounded method and comparing it with standard VIM, it was concluded that complete reliability, efficiency, and accuracy of this method are guaranteed. Additionally, we studied and investigated the convergence of the proposed method, namely the VIM with an auxiliary parameter. We also offered the optimal choice of the auxiliary parameter in the proposed method. It was noticed that the approach could be applied to other models of physics.

Suggested Citation

  • Mohammad Abolhasani & Saeid Abbasbandy & Tofigh Allahviranloo, 2017. "A New Variational Iteration Method for a Class of Fractional Convection-Diffusion Equations in Large Domains," Mathematics, MDPI, vol. 5(2), pages 1-15, May.
    • Handle: RePEc:gam:jmathe:v:5:y:2017:i:2:p:26-:d:98295
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    References listed on IDEAS

    as
    1. Abbasbandy, Saeid & Kazem, Saeed & Alhuthali, Mohammed S. & Alsulami, Hamed H., 2015. "Application of the operational matrix of fractional-order Legendre functions for solving the time-fractional convection–diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 31-40.
    2. Hongliang Liu & Aiguo Xiao & Lihong Su, 2013. "Convergence of Variational Iteration Method for Second-Order Delay Differential Equations," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-9, February.
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