IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v218y2024icp544-555.html
   My bibliography  Save this article

Fourier-Gegenbauer pseudospectral method for solving time-dependent one-dimensional fractional partial differential equations with variable coefficients and periodic solutions

Author

Listed:
  • Elgindy, Kareem T.

Abstract

In this paper, we present a novel pseudospectral (PS) method for solving a new class of initial-value problems (IVPs) of time-dependent one-dimensional fractional partial differential equations (FPDEs) with variable coefficients and periodic solutions. A main ingredient of our work is the use of the recently developed periodic RL/Caputo fractional derivative (FD) operators with sliding positive fixed memory length of Bourafaet al. (2021) or their reduced forms obtained by Elgindy (2023) as the natural FD operators to accurately model FPDEs with periodic solutions. The proposed method converts the IVP into a well-conditioned linear system of equations using the PS method based on Fourier collocations and Gegenbauer quadratures. The reduced linear system has a simple special structure and can be solved accurately and rapidly by using standard linear system solvers. A rigorous study of the computational storage requirements as well as the error and convergence of the proposed method is presented. The idea and results presented in this paper are expected to be useful in the future to address more general problems involving FPDEs with periodic solutions.

Suggested Citation

  • Elgindy, Kareem T., 2024. "Fourier-Gegenbauer pseudospectral method for solving time-dependent one-dimensional fractional partial differential equations with variable coefficients and periodic solutions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 218(C), pages 544-555.
    • Handle: RePEc:eee:matcom:v:218:y:2024:i:c:p:544-555
    DOI: 10.1016/j.matcom.2023.11.034
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475423004950
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2023.11.034?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:eee:matcom:v:218:y:2024:i:c:p:544-555. 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: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.