IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i9p1440-d404962.html
   My bibliography  Save this article

The Convergence Analysis of a Numerical Method for a Structured Consumer-Resource Model with Delay in the Resource Evolution Rate

Author

Listed:
  • Luis M. Abia

    (Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Valladolid e IMUVa, 47011 Valladolid, Spain)

  • Óscar Angulo

    (Departamento de Matemática Aplicada, ETS de Ingenieros de Telecomunicación, Universidad de Valladolid e IMUVa, 47011 Valladolid, Spain)

  • Juan C. López-Marcos

    (Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Valladolid e IMUVa, 47011 Valladolid, Spain)

  • Miguel A. López-Marcos

    (Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Valladolid e IMUVa, 47011 Valladolid, Spain)

Abstract

In this paper, we go through the development of a new numerical method to obtain the solution to a size-structured population model that describes the evolution of a consumer feeding on a dynamical resource that reacts to the environment with a lag-time response. The problem involves the coupling of the partial differential equation that represents the population evolution and an ordinary differential equation with a constant delay that describes the evolution of the resource. The numerical treatment of this problem has not been considered before when a delay is included in the resource evolution rate. We analyzed the numerical scheme and proved a second-order rate of convergence by assuming enough regularity of the solution. We numerically confirmed the theoretical results with an academic test problem.

Suggested Citation

  • Luis M. Abia & Óscar Angulo & Juan C. López-Marcos & Miguel A. López-Marcos, 2020. "The Convergence Analysis of a Numerical Method for a Structured Consumer-Resource Model with Delay in the Resource Evolution Rate," Mathematics, MDPI, vol. 8(9), pages 1-18, August.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:9:p:1440-:d:404962
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/9/1440/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/9/1440/
    Download Restriction: no
    ---><---

    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:gam:jmathe:v:8:y:2020:i:9:p:1440-:d:404962. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.