IDEAS home Printed from https://ideas.repec.org/a/bpj/mcmeap/v30y2024i3p235-248n1003.html
   My bibliography  Save this article

Random walk algorithms for solving nonlinear chemotaxis problems

Author

Listed:
  • Sabelfeld Karl K.

    (Institute of Computational Mathematics and Mathematical Geophysics, Russian Academy of Sciences, Novosibirsk, Russia)

  • Bukhasheev Oleg

    (Novosibirsk State University, Pirogova str. 2, 630090 Novosibirsk, Russia)

Abstract

Random walk based stochastic simulation methods for solving a nonlinear system of coupled transient diffusion and drift-diffusion equations governing a two-component chemotaxis process are developed. The nonlinear system is solved by linearization, the system is evolved in time, by small time steps, where on each step a linear system of equations is solved by using the solution from the previous time step. Three different stochastic algorithms are suggested, (1) the global random walk on grid (GRWG), (2) a randomized vector algorithm (RVA) based on a special transformation of the original matrix to a stochastic matrix, and (3) a stochastic projection algorithm (SPA). To get high precision results, these methods are combined with an iterative refinement method.

Suggested Citation

  • Sabelfeld Karl K. & Bukhasheev Oleg, 2024. "Random walk algorithms for solving nonlinear chemotaxis problems," Monte Carlo Methods and Applications, De Gruyter, vol. 30(3), pages 235-248.
    • Handle: RePEc:bpj:mcmeap:v:30:y:2024:i:3:p:235-248:n:1003
    DOI: 10.1515/mcma-2024-2008
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/mcma-2024-2008
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.1515/mcma-2024-2008?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:bpj:mcmeap:v:30:y:2024:i:3:p:235-248:n:1003. 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: Peter Golla (email available below). General contact details of provider: https://www.degruyter.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.