IDEAS home Printed from https://ideas.repec.org/a/wsi/ijmpcx/v32y2021i09ns0129183121501187.html
   My bibliography  Save this article

Shifted Gegenbauer–Galerkin algorithm for hyperbolic telegraph type equation

Author

Listed:
  • H. T. Taghian

    (Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt)

  • W. M. Abd-Elhameed

    (#x2020;Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt)

  • G. M. Moatimid

    (Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt)

  • Y. H. Youssri

    (#x2020;Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt)

Abstract

This paper is concerned with a numerical spectral solution to a one-dimensional linear telegraph type equation with constant coefficients. An efficient Galerkin algorithm is implemented and analyzed for treating this type of equations. The philosophy of utilization of the Galerkin method is built on picking basis functions that are consistent with the corresponding boundary conditions of the telegraph type equation. A suitable combination of the orthogonal shifted Gegenbauer polynomials is utilized. The proposed method produces systems of especially inverted matrices. Furthermore, the convergence and error analysis of the proposed expansion are investigated. This study was built on assuming that the solution to the problem is separable. The paper ends by checking the applicability and effectiveness of the proposed algorithm by solving some numerical examples.

Suggested Citation

  • H. T. Taghian & W. M. Abd-Elhameed & G. M. Moatimid & Y. H. Youssri, 2021. "Shifted Gegenbauer–Galerkin algorithm for hyperbolic telegraph type equation," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 32(09), pages 1-20, September.
    • Handle: RePEc:wsi:ijmpcx:v:32:y:2021:i:09:n:s0129183121501187
    DOI: 10.1142/S0129183121501187
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0129183121501187
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0129183121501187?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. Ahmed, Hoda F. & Hashem, W.A., 2023. "A fully spectral tau method for a class of linear and nonlinear variable-order time-fractional partial differential equations in multi-dimensions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 214(C), pages 388-408.

    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:32:y:2021:i:09:n:s0129183121501187. 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.