IDEAS home Printed from https://ideas.repec.org/a/hin/jnijde/852919.html
   My bibliography  Save this article

Solutions of the Force-Free Duffing-van der Pol Oscillator Equation

Author

Listed:
  • Najeeb Alam Khan
  • Muhammad Jamil
  • Syed Anwar Ali
  • Nadeem Alam Khan

Abstract

A new approximate method for solving the nonlinear Duffing-van der pol oscillator equation is proposed. The proposed scheme depends only on the two components of homotopy series, the Laplace transformation and, the Padé approximants. The proposed method introduces an alternative framework designed to overcome the difficulty of capturing the behavior of the solution and give a good approximation to the solution for a large time. The Runge-Kutta algorithm was used to solve the governing equation via numerical solution. Finally, to demonstrate the validity of the proposed method, the response of the oscillator, which was obtained from approximate solution, has been shown graphically and compared with that of numerical solution.

Suggested Citation

  • Najeeb Alam Khan & Muhammad Jamil & Syed Anwar Ali & Nadeem Alam Khan, 2011. "Solutions of the Force-Free Duffing-van der Pol Oscillator Equation," International Journal of Differential Equations, Hindawi, vol. 2011, pages 1-9, October.
    • Handle: RePEc:hin:jnijde:852919
    DOI: 10.1155/2011/852919
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/IJDE/2011/852919.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/IJDE/2011/852919.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2011/852919?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ruiz, A. & Muriel, C., 2018. "On the integrability of Liénard I-type equations via λ-symmetries and solvable structures," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 888-898.

    More about this item

    Statistics

    Access and download statistics

    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:hin:jnijde:852919. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.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.