IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v62y2003i3p487-494.html
   My bibliography  Save this article

A quasi-random walk method for one-dimensional reaction–diffusion equations

Author

Listed:
  • Ogawa, S.
  • Lécot, C.

Abstract

Probabilistic methods are presented to solve one-dimensional nonlinear reaction–diffusion equations. Computational particles are used to approximate the spatial derivative of the solution. The random walk principle is used to model the diffusion term. We investigate the effect of replacing pseudo-random numbers by quasi-random numbers in the random walk steps. This cannot be implemented in a straightforward fashion, because of correlations. If the particles are reordered according to their position at each time step, this has the effect of breaking correlations. For simple demonstration problems, the error is found to be significantly less when quasi-random sequences are used than when a standard random walk calculation is performed using pseudo-random points.

Suggested Citation

  • Ogawa, S. & Lécot, C., 2003. "A quasi-random walk method for one-dimensional reaction–diffusion equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 62(3), pages 487-494.
    • Handle: RePEc:eee:matcom:v:62:y:2003:i:3:p:487-494
    DOI: 10.1016/S0378-4754(02)00243-4
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475402002434
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/S0378-4754(02)00243-4?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.

    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:3:p:487-494. 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.