IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v5y2017i2p26-d98295.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/5/2/26/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/5/2/26/
    Download Restriction: no
    ---><---

    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sun, Lin & Chen, Yiming & Dang, Rongqi & Cheng, Gang & Xie, Jiaquan, 2022. "Shifted Legendre polynomials algorithm used for the numerical analysis of viscoelastic plate with a fractional order model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 190-203.
    2. Dehestani, H. & Ordokhani, Y. & Razzaghi, M., 2018. "Fractional-order Legendre–Laguerre functions and their applications in fractional partial differential equations," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 433-453.
    3. Zhou, Quan & Wang, Yinkun & Liu, Yicheng, 2024. "Chebyshev–Picard iteration methods for solving delay differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 217(C), pages 1-20.
    4. Hashemi, M.S. & Atangana, A. & Hajikhah, S., 2020. "Solving fractional pantograph delay equations by an effective computational method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 177(C), pages 295-305.
    5. Behroozifar, M. & Sazmand, A., 2017. "An approximate solution based on Jacobi polynomials for time-fractional convection–diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 296(C), pages 1-17.
    6. Hashemi, M.S., 2021. "A novel approach to find exact solutions of fractional evolution equations with non-singular kernel derivative," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:5:y:2017:i:2:p:26-:d:98295. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.