IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v62y2003i1p125-135.html
   My bibliography  Save this article

Non-linear evolution using optimal fourth-order strong-stability-preserving Runge–Kutta methods

Author

Listed:
  • Spiteri, Raymond J.
  • Ruuth, Steven J.

Abstract

Strong-stability-preserving (SSP) time discretization methods (also known as total-variation-diminishing or TVD methods) are popular and effective algorithms for the simulation of partial differential equations having discontinuous or shock-like solutions. Optimal SSP Runge–Kutta (SSPRK) schemes have been previously found for methods with up to five stages and up to fourth order. In this paper, we present new optimal fourth-order SSPRK schemes with mild storage requirements and up to eight stages. We find that these schemes are ultimately more efficient than the known fourth-order SSPRK schemes because the increase in the allowable time-step more than offsets the added computational expense per step. We demonstrate these efficiencies on a pair of scalar conservation laws.

Suggested Citation

  • Spiteri, Raymond J. & Ruuth, Steven J., 2003. "Non-linear evolution using optimal fourth-order strong-stability-preserving Runge–Kutta methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 62(1), pages 125-135.
    • Handle: RePEc:eee:matcom:v:62:y:2003:i:1:p:125-135
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475402001799
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    More about this item

    Keywords

    Evolution; Optimal; SSP;
    All these 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:eee:matcom:v:62:y:2003:i:1:p:125-135. 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.