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

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  • 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
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
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