A convergence analysis for the approximation to the solution of an age-structured population model with infinite lifespan

IF 5.4 3区材料科学 Q2 CHEMISTRY, PHYSICAL

ACS Applied Energy Materials Pub Date : 2024-10-16 DOI:10.1016/j.matcom.2024.10.007

Luis M. Abia, Óscar Angulo, Juan Carlos López-Marcos, Miguel Ángel López-Marcos

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引用次数: 0

Abstract

Considering the numerical approximation of the density distribution for an age-structured population model with unbounded lifespan on a compact interval

[0, T]

, we prove second order of convergence for a discretization that adaptively selects its truncated age-interval according to the exponential rate of decay with age of the solution of the model. It appears that the adaptive capacity of the length in the truncated age-interval of the discretization to the infinity lifespan is a very convenient approach for a long-time integration of the model to establish the asymptotic behavior of its dynamics numerically. The analysis of convergence uses an appropriate weighted maximum norm with exponential weights to cope with the unbounded age lifespan. We report experiments to exhibit numerically the theoretical results and the asymptotic behavior of the dynamics for an age-structured squirrel population model introduced by Sulsky.

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寿命无限的年龄结构人口模型近似解的收敛性分析

考虑到在紧凑区间 [0,T] 上对寿命无限制的年龄结构人口模型的密度分布进行数值近似，我们证明了根据模型解随年龄的指数衰减率自适应选择截断年龄区间的离散化的二阶收敛性。看来，离散化的截断年龄区间长度对无穷大寿命的自适应能力是对模型进行长时间积分的一种非常方便的方法，可以在数值上确定其动态的渐近行为。收敛分析使用了适当的指数加权最大规范，以应对无限制的年龄寿命。我们报告了实验结果，以数值形式展示了 Sulsky 引入的年龄结构松鼠种群模型的理论结果和动力学渐近行为。

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来源期刊

ACS Applied Energy Materials Materials Science-Materials Chemistry

CiteScore

10.30

自引率

6.20%

发文量

1368

期刊介绍： ACS Applied Energy Materials is an interdisciplinary journal publishing original research covering all aspects of materials, engineering, chemistry, physics and biology relevant to energy conversion and storage. The journal is devoted to reports of new and original experimental and theoretical research of an applied nature that integrate knowledge in the areas of materials, engineering, physics, bioscience, and chemistry into important energy applications.