IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v81y2011i9p1707-1728.html
   My bibliography  Save this article

Construction and implementation of highly stable two-step continuous methods for stiff differential systems

Author

Listed:
  • D’Ambrosio, Raffaele
  • Jackiewicz, Zdzislaw

Abstract

We describe a class of two-step continuous methods for the numerical integration of initial-value problems based on stiff ordinary differential equations (ODEs). These methods generalize the class of two-step Runge-Kutta methods. We restrict our attention to methods of order p=m, where m is the number of internal stages, and stage order q=p to avoid order reduction phenomenon for stiff equations, and determine some of the parameters to reduce the contribution of high order terms in the local discretization error. Moreover, we enforce the methods to be A-stable and L-stable. The results of some fixed and variable stepsize numerical experiments which indicate the effectiveness of two-step continuous methods and reliability of local error estimation will also be presented.

Suggested Citation

  • D’Ambrosio, Raffaele & Jackiewicz, Zdzislaw, 2011. "Construction and implementation of highly stable two-step continuous methods for stiff differential systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(9), pages 1707-1728.
    • Handle: RePEc:eee:matcom:v:81:y:2011:i:9:p:1707-1728
    DOI: 10.1016/j.matcom.2011.01.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475411000334
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2011.01.005?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. Chang, Shuenn-Yih, 2022. "A family of matrix coefficient formulas for solving ordinary differential equations," Applied Mathematics and Computation, Elsevier, vol. 418(C).

    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:81:y:2011:i:9:p:1707-1728. 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.