IDEAS home Printed from https://ideas.repec.org/a/hin/jnlmpe/878497.html
   My bibliography  Save this article

On the Computation of Blow-Up Solutions for Nonlinear Volterra Integrodifferential Equations

Author

Listed:
  • P. G. Dlamini
  • M. Khumalo

Abstract

We make use of an adaptive numerical method to compute blow-up solutions for nonlinear ordinary Volterra integrodifferential equations (VIDEs). The method is based on the implicit midpoint method and the implicit Euler method and is named the implicit midpoint-implicit Euler (IMIE) method and was used to compute blow-up solutions in semilinear ODEs and parabolic PDEs in our earlier work. We demonstrate that the method produces superior results to the adaptive PECE-implicit Euler (PECE-IE) method and the MATLAB solver of comparable order just as it did in our previous contribution. We use quadrature rules to approximate the integral in the VIDE and demonstrate that the choice of quadrature rule has a significant effect on the blow-up time computed. In cases where the problem contains a convolution kernel with a singularity we use convolution quadrature.

Suggested Citation

  • P. G. Dlamini & M. Khumalo, 2012. "On the Computation of Blow-Up Solutions for Nonlinear Volterra Integrodifferential Equations," Mathematical Problems in Engineering, Hindawi, vol. 2012, pages 1-11, May.
    • Handle: RePEc:hin:jnlmpe:878497
    DOI: 10.1155/2012/878497
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/MPE/2012/878497.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/MPE/2012/878497.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2012/878497?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
    ---><---

    More about this item

    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:hin:jnlmpe:878497. 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: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.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.