带资源项的随机尺度结构系统数值收敛性分析
Numerical Convergence Analysis of Stochastic Size-Structured Models with Resource Term
DOI: 10.12677/AAM.2023.125233, PDF,    国家自然科学基金支持
作者: 卫烁遥, 李 心*：燕山大学理学院，河北 秦皇岛
关键词: Markovian转换；随机种群；尺度结构；半隐式欧拉；收敛性；Markovian Transformation； Random Population； Scale Structure； Semi-Implicit Euler； Convergence
摘要: 种群研究作为生物研究的重要组成部分之一，在生物发展进程中起着至关重要的作用。文章考虑了一类带有特殊资源项和随机因素的尺度结构系统数值解的收敛性问题。首先，利用半隐式欧拉数值方法，构造离散模型的数值解；随后，在一定的假设条件下，利用Itô引理，讨论了该系统数值解的依均方收敛性；最后，根据离散系统的特点对带有尺度结构的随机种群模型进行了数值模拟，同时验证数值方法的可靠性。
Abstract: Population research plays an important role in biological research as an important part of biological research. The convergence of numerical solutions for a class of scale-structured systems with special resource terms and random factors is considered in this paper. First, the numerical solutions of dis-crete models are constructed by using semi-implicit Euler numerical methods. Then, under certain assumptions, the mean-square convergence of the numerical solution of the system is discussed using the Itô lemma. Finally, the stochastic population model with size-structure is simulated nu-merically according to the characteristics of the discrete system, and the reliability of the numerical method is verified.
文章引用：卫烁遥, 李心. 带资源项的随机尺度结构系统数值收敛性分析[J]. 应用数学进展, 2023, 12(5): 2288-2302. https://doi.org/10.12677/AAM.2023.125233

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