IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v182y2021icp603-619.html
   My bibliography  Save this article

Numerical analysis of linear θ-methods with two-layer boundary conditions for age-structured population models

Author

Listed:
  • Chen, Zhijie
  • Xu, Runze
  • Yang, Zhanwen

Abstract

In this paper, we consider a fully discretization scheme for infinite age-structured population models with time-variable fertility rate and mortality rate. Based on the characteristics, the classical linear θ-methods with a kind of two-layer boundary condition are constructed for preserving an invariance of total populations. We are interested in the finite-time convergence and the stability for a long time. With the classical approach, some conjecture on the first order convergence is proved. For the time-independent model the numerical stability is studied by an embedded infinite dimensional dynamical system, which provides a numerical basic reproduction number by the infinite Leslie operator. Furthermore, it is shown that the numerical solutions replicate the un-stability and stability of the analytical solutions for small stepsize. Finally, three examples are given to verify the feasibility of our methods.

Suggested Citation

  • Chen, Zhijie & Xu, Runze & Yang, Zhanwen, 2021. "Numerical analysis of linear θ-methods with two-layer boundary conditions for age-structured population models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 603-619.
    • Handle: RePEc:eee:matcom:v:182:y:2021:i:c:p:603-619
    DOI: 10.1016/j.matcom.2020.11.016
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475420304109
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2020.11.016?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.

    References listed on IDEAS

    as
    1. Akimenko, Vitalii V., 2017. "Asymptotically stable states of nonlinear age-structured monocyclic population model I. Travelling wave solution," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 133(C), pages 2-23.
    2. Marinoschi, Gabriela & Martiradonna, Angela, 2016. "Fish populations dynamics with nonlinear stock-recruitment renewal conditions," Applied Mathematics and Computation, Elsevier, vol. 277(C), pages 101-110.
    3. Akimenko, Vitalii V., 2017. "Asymptotically stable states of non-linear age-structured monocyclic population model II. Numerical simulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 133(C), pages 24-38.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Huang, Chengdai & Li, Huan & Cao, Jinde, 2019. "A novel strategy of bifurcation control for a delayed fractional predator–prey model," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 808-838.
    2. Zhe Yin & Yongguang Yu & Zhenzhen Lu, 2020. "Stability Analysis of an Age-Structured SEIRS Model with Time Delay," Mathematics, MDPI, vol. 8(3), pages 1-17, March.

    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:182:y:2021:i:c:p:603-619. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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.