In this study, we study a nonlinear age-structured population models with discontinues mortality and fertility rates, motivated by the fact that different maturation period may cause the significant difference in rates. We develop a novel numerical method with two-layer boundary conditions, the linearly implicit θ-methods on a special mesh. With a uniform boundedness analysis of numerical solutions, the finite time convergence is proved piecewisely according to the fundamental approach for the smooth rates. For juvenile-adult models, the existence of numerical endemic equilibrium is determined by a numerical basic reproduction function, which converges to the exact one with accuracy of order 1. Moreover, it is shown that for juvenile-adult models, the global stability of the disease-free equilibrium and the local stability of the endemic equilibrium are approximately exhibited by the numerical processes. Finally, some numerical experiments on the Logistic models and tadpoles-frogs models illustrate the verification and the efficiency of our results.

中文翻译：

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不连续非线性 Gurtin-MacCamy 模型的线性隐式方法的数值分析。

在这项研究中，我们研究了一个非线性年龄结构的人口模型，该模型具有中断死亡率和生育率，其动机是不同的成熟期可能导致比率的显着差异。我们开发了一种具有双层边界条件的新型数值方法，即特殊网格上的线性隐式 θ 方法。通过数值解的一致有界分析，根据平滑率的基本方法分段证明了有限时间收敛性。对于青少年-成人模型，数值地方病平衡的存在性由数值基本繁殖函数决定，该函数收敛到准确度为 1 的精确函数。此外，对于青少年-成人模型，结果表明，无病平衡的全局稳定性和地方病平衡的局部稳定性由数值过程近似地表现出来。最后，对Logistic模型和蝌蚪-青蛙模型的一些数值实验说明了我们结果的验证和有效性。