 Numerical analysis of linear θ-methods with two-layer boundary conditions for age-structured population modelsZhijie Chen, Runze Xu and Zhanwen Yang Mathematics and Computers in Simulation (MATCOM), 2021, vol. 182, issue C, 603-619 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. Keywords: Age-structured population models; Linear θ-methods; Leslie matrix; Basic reproduction number (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:182:y:2021:i:c:p:603-619 DOI: 10.1016/j.matcom.2020.11.016 Access Statistics for this article Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier |
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