IDEAS home Printed from https://ideas.repec.org/a/wsi/fracta/v31y2023i02ns0218348x23400182.html
   My bibliography  Save this article

A Hybrid Numerical Technique For Solving Three-Dimensional Second-Order Parabolic Partial Differential Equations

Author

Listed:
  • MUHAMMAD ASIF

    (Department of Mathematics, University of Peshawar, Peshawar, Pakistan)

  • ROHUL AMIN

    (Department of Mathematics, University of Peshawar, Peshawar, Pakistan)

  • NADEEM HAIDER

    (Department of Mathematics, University of Peshawar, Peshawar, Pakistan)

  • IMRAN KHAN

    (Department of Mathematics, University of Peshawar, Peshawar, Pakistan)

  • QASEM M. AL-MDALLAL

    (Department of Mathematical Sciences, UAE University, P. O. Box 15551, Al Ain, UAE)

  • SALEM BEN SAID

    (Department of Mathematical Sciences, UAE University, P. O. Box 15551, Al Ain, UAE)

Abstract

In this paper, a hybrid approach is presented for the numerical solution of three-dimensional parabolic partial differential equations. This new approach is applicable to both linear and nonlinear parabolic problems including systems. This hybrid numerical technique is based on the Haar wavelet collocation technique and the finite difference method. In this technique, the space derivative is approximated by truncated Haar wavelet series whereas the time derivative is approximated by finite difference method. The aforementioned proposed algorithms are very simple and can easily be implemented in any computer-oriented language efficiently. In order to demonstrate the efficiency and better accuracy of the newly developed numerical technique it is applied to some well-known examples from previous literature that comprises linear and nonlinear three-dimensional parabolic equations including systems. The obtained results affirm better accuracy and widespread applicability of the newly proposed numerical technique for a range of benchmark problems.

Suggested Citation

  • Muhammad Asif & Rohul Amin & Nadeem Haider & Imran Khan & Qasem M. Al-Mdallal & Salem Ben Said, 2023. "A Hybrid Numerical Technique For Solving Three-Dimensional Second-Order Parabolic Partial Differential Equations," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(02), pages 1-16.
    • Handle: RePEc:wsi:fracta:v:31:y:2023:i:02:n:s0218348x23400182
    DOI: 10.1142/S0218348X23400182
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0218348X23400182
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0218348X23400182?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:fracta:v:31:y:2023:i:02:n:s0218348x23400182. 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: https://www.worldscientific.com/worldscinet/fractals .

    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.