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.

中文翻译：

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用于年龄结构人口模型的具有两层边界条件的线性 θ 方法的数值分析

摘要 在本文中，我们考虑了具有时变生育率和死亡率的无限年龄结构人口模型的完全离散化方案。基于这些特点，构造了具有一种两层边界条件的经典线性θ-方法来保持总种群的不变性。我们对有限时间收敛性和长时间稳定性感兴趣。用经典方法，证明了关于一阶收敛的一些猜想。对于时间无关模型，数值稳定性由嵌入式无限维动力系统研究，该系统通过无限 Leslie 算子提供数值基本再现数。此外，它表明数值解复制了小步长解析解的不稳定和稳定性。