IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-981-4585-33-0_29.html
   My bibliography  Save this book chapter

Implicit Finite Difference Solutions of One-Dimensional Burgers’ Equation Using Newton–HSSOR Method

In: International Conference on Mathematical Sciences and Statistics 2013

Author

Listed:
  • J. Sulaiman

    (Universiti Malaysia Sabah, Mathematics with Economics Programme)

  • M. K. Hasan

    (Universiti Kebangsaan Malaysia, School of Information Technology)

  • M. Othman

    (Universiti Putra Malaysia, Department of Communication Technology and Network)

  • S.A.A. Karim

    (Universiti Teknologi Petronas, Fundamental and Applied Sciences Department)

Abstract

In this paper, we present the application of half-sweep successive over-relaxation (HSSOR) iterative methods together with Newton scheme, collectively Newton–HSSOR, in solving the nonlinear systems generated from the half-sweep Crank–Nicolson finite difference discretization scheme for a one-dimensional Burgers’ equation. To linearize nonlinear systems, the Newton scheme is proposed to transform the nonlinear system into the form of linear system. In addition to that, the basic formulation and implementation of Newton–HSSOR iterative method are also shown. For comparison purpose, we also consider combinations between the full-sweep Gauss–Seidel (FSGS) and full-sweep successive over-relaxation (FSSOR) iterative methods with Newton scheme, which are indicated as Newton–FSGS and Newton–FSSOR methods respectively. Consequently, two illustrative examples are included to demonstrate the validity and applicability of tested methods. Finally, it can be concluded that the Newton–HSSOR method shows superiority over other tested methods.

Suggested Citation

  • J. Sulaiman & M. K. Hasan & M. Othman & S.A.A. Karim, 2014. "Implicit Finite Difference Solutions of One-Dimensional Burgers’ Equation Using Newton–HSSOR Method," Springer Books, in: Adem Kilicman & Wah June Leong & Zainidin Eshkuvatov (ed.), International Conference on Mathematical Sciences and Statistics 2013, edition 127, pages 285-295, Springer.
    • Handle: RePEc:spr:sprchp:978-981-4585-33-0_29
    DOI: 10.1007/978-981-4585-33-0_29
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:spr:sprchp:978-981-4585-33-0_29. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.