时滞微分方程特征值的近似求解方法

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振动与冲击 ›› 2010, Vol. 29 ›› Issue (5) : 31-34.

论文

时滞微分方程特征值的近似求解方法

徐鉴1;刘隆2

作者信息 +

An Approximate Method for Calculating Eigenvalues of Delay Differential Equation

Xu Jian;Liu Long

Author information +

文章历史 +

摘要

通过将时滞微分方程变换为积分方程后并进行离散，得到相应的差分方程，从理论上建立了差分方程的系统矩阵的特征值与原线性时滞微分系统的特征值之间的关系，从而得到了一种求解时滞微分方程特征值的新方法。作为算例，计算了时滞的Logistic方程的前10阶特征值。误差分析表明，本文提出的近似方法不但简单，并且有很高的精度。

Abstract

The delay differential equation is first changed to be an integral equation. The corresponding difference equation is obtained by the discrete integral equation. The relation between the eigenvalues of the discrete difference and the delay differential equation is presented analytically. It yields that a new approximate method is proposed to calculate eigenvalues of the delayed differential equation. As an example, the first ten-order eigenvalues are computed for an delayed Logistic equation. The results with the error estimation show the present method provides not only simple steps but also high accuracy.

导出引用

徐鉴;刘隆. 时滞微分方程特征值的近似求解方法[J]. 振动与冲击, 2010, 29(5): 31-34

Xu Jian;Liu Long . An Approximate Method for Calculating Eigenvalues of Delay Differential Equation[J]. Journal of Vibration and Shock, 2010, 29(5): 31-34