IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v271y2015icp436-445.html
   My bibliography  Save this article

Periodic analytic approximate solutions for the Mathieu equation

Author

Listed:
  • Gadella, M.
  • Giacomini, H.
  • Lara, L.P.

Abstract

We propose two methods to find analytic periodic approximations intended for differential equations of Hill type. Here, we apply these methods on the simplest case of the Mathieu equation. The former has been inspired in the harmonic balance method and designed to find, making use on a given algebraic function, analytic approximations for the critical values and their corresponding periodic solutions of the Mathieu differential equation. What is new is that these solutions are valid for all values of the equation parameter q, no matter how large. The second one uses truncations of Fourier series and has connections with the least squares method.

Suggested Citation

  • Gadella, M. & Giacomini, H. & Lara, L.P., 2015. "Periodic analytic approximate solutions for the Mathieu equation," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 436-445.
    • Handle: RePEc:eee:apmaco:v:271:y:2015:i:c:p:436-445
    DOI: 10.1016/j.amc.2015.09.018
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300315012369
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2015.09.018?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

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


    Cited by:

    1. Chein-Shan Liu & Yung-Wei Chen, 2021. "A Simplified Lindstedt-Poincaré Method for Saving Computational Cost to Determine Higher Order Nonlinear Free Vibrations," Mathematics, MDPI, vol. 9(23), pages 1-17, November.
    2. Chein-Shan Liu, 2020. "Analytic Solutions of the Eigenvalues of Mathieu’s Equation," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 12(1), pages 1-1, February.

    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:eee:apmaco:v:271:y:2015:i:c:p:436-445. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.