IDEAS home Printed from https://ideas.repec.org/a/wsi/ijmpcx/v31y2020i07ns012918312050093x.html
   My bibliography  Save this article

Hermite collocation method for obtaining the chaotic behavior of a nonlinear coupled system of FDEs

Author

Listed:
  • M. M. Khader

    (Department of Mathematics and Statistics, College of Science, Imam Mohammad, Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia†Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt)

  • Mohammed M. Babatin

    (Department of Mathematics and Statistics, College of Science, Imam Mohammad, Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia)

Abstract

This paper is devoted to introduce an efficient solver using the Hermite collocation technique (HCT), of the coupled system of fractional differential equations (FDEs). The given systems are of basic importance in modeling various phenomena like Cascades and Compartment Analysis, Pond Pollution, Home Heating, Chemostats, and Microorganism Culturing, Nutrient Flow in an Aquarium, Biomass Transfer, Forecasting Prices, Electrical Network, Earthquake Effects on Buildings. The proposed method reduces the system of FDEs to a system of algebraic equations in the coefficients of the expansion using the Hermite polynomials. The introduced method is computer oriented and provides highly accurate solution. To demonstrate the efficiency of the method, two examples are solved and the results are displayed graphically. Finally, we convert the presented coupled systems from the case of its standard form to a first-order ordinary differential equations to compare the obtained numerical solutions with those solutions using the fourth-order Runge–Kutta method (RK4).

Suggested Citation

  • M. M. Khader & Mohammed M. Babatin, 2020. "Hermite collocation method for obtaining the chaotic behavior of a nonlinear coupled system of FDEs," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 31(07), pages 1-12, July.
    • Handle: RePEc:wsi:ijmpcx:v:31:y:2020:i:07:n:s012918312050093x
    DOI: 10.1142/S012918312050093X
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S012918312050093X
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S012918312050093X?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.

    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:wsi:ijmpcx:v:31:y:2020:i:07:n:s012918312050093x. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/ijmpc/ijmpc.shtml .

    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.