IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v314y2017icp380-390.html
   My bibliography  Save this article

On A-stable one-leg methods for solving nonlinear Volterra functional differential equations

Author

Listed:
  • Wang, Wansheng

Abstract

This paper is concerned with the stability of the one-leg methods for nonlinear Volterra functional differential equations (VFDEs). The contractivity and asymptotic stability properties are first analyzed for quasi-equivalent and A-stable one-leg methods by use of two lemmas proven in this paper. To extend the analysis to the case of strongly A-stable one-leg methods, Nevanlinna and Liniger’s technique of introducing new norm is used to obtain the conditions for contractivity and asymptotic stability of these methods. As a consequence, it is shown that one-leg θ-methods (θ ∈ (1/2, 1]) with linear interpolation are unconditionally contractive and asymptotically stable, and 2-step Adams type method and 2-step BDF method are conditionally contractive and asymptotically stable. The bounded stability of the midpoint rule is also proved with the help of the concept of semi-equivalent one-leg methods.

Suggested Citation

  • Wang, Wansheng, 2017. "On A-stable one-leg methods for solving nonlinear Volterra functional differential equations," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 380-390.
    • Handle: RePEc:eee:apmaco:v:314:y:2017:i:c:p:380-390
    DOI: 10.1016/j.amc.2017.07.013
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300317304642
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2017.07.013?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. Zhou, Yongtao & Zhang, Chengjian, 2019. "One-leg methods for nonlinear stiff fractional differential equations with Caputo derivatives," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 594-608.

    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:apmaco:v:314:y:2017:i:c:p:380-390. 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: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.