基于复合Heun方法的不确定延迟微分方程的最小二乘估计
Least Squares Estimation of Uncertain Delay Differential Equations Based on the Composite Heun Method
摘要: 文章基于复合Heun方法，研究了不确定延迟微分方程的最小二乘估计问题。利用复合Heun方法，建立了不确定延迟微分方程的差分形式，从而将漂移项中参数的估计问题转化为优化问题，扩散项中参数的估计问题转化为方程的求解。数值算例表明，复合Heun方法的最小二乘估计计算结果优于传统的欧拉方法。最后，利用本文提出的参数估计方法对美洲鹤种群进行了建模分析。
Abstract: Based on the composite Heun method, the article investigates the least squares estimation problem for uncertain delay differential equations. By utilizing the composite Heun method, a difference form is established for uncertain delay differential equations. Then the parameter estimation problem in the drift term is transformed into an optimization problem, and the parameter estimation problem in the diffusion term is converted to solve a system of equations. Numerical examples demonstrate that the least squares estimation using the composite Heun method outperforms the conventional Euler method. Finally, a modeling analysis of the population dynamics of whooping cranes is conducted by applying the parameter estimation method developed in this study.
文章引用：刘持腾, 周少玲. 基于复合Heun方法的不确定延迟微分方程的最小二乘估计[J]. 应用数学进展, 2025, 14(4): 525-535. https://doi.org/10.12677/aam.2025.144183

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