IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v296y2017icp101-115.html
   My bibliography  Save this article

A parameter uniform difference scheme for singularly perturbed parabolic delay differential equation with Robin type boundary condition

Author

Listed:
  • Avudai Selvi, P.
  • Ramanujam, N.

Abstract

A Robin type boundary value problem for a singularly perturbed parabolic delay differential equation is studied on a rectangular domain in the x - t plane. The second-order space derivative is multiplied by a small parameter, which gives rise to parabolic boundary layers on the two lateral sides of the rectangle. A numerical method comprising a standard finite difference scheme on a rectangular piecewise uniform fitted mesh of Nx × Nt elements condensing in the boundary layers is suggested and it is proved to be parameter-uniform. More specifically, it is shown that the errors are bounded in the maximum norm by C(Nx−2ln2Nx+Nt−1), where C is a constant independent of Nx, Nt and the small parameter. To validate the theoretical result an example is provided.

Suggested Citation

  • Avudai Selvi, P. & Ramanujam, N., 2017. "A parameter uniform difference scheme for singularly perturbed parabolic delay differential equation with Robin type boundary condition," Applied Mathematics and Computation, Elsevier, vol. 296(C), pages 101-115.
    • Handle: RePEc:eee:apmaco:v:296:y:2017:i:c:p:101-115
    DOI: 10.1016/j.amc.2016.10.027
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300316306257
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2016.10.027?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. Kumar, Sunil & Sumit, & Ramos, Higinio, 2021. "Parameter-uniform approximation on equidistributed meshes for singularly perturbed parabolic reaction-diffusion problems with Robin boundary conditions," Applied Mathematics and Computation, Elsevier, vol. 392(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:apmaco:v:296:y:2017:i:c:p:101-115. 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.