• 论文 •

### 二阶延迟微分方程θ-方法的TH-稳定性

1. 哈尔滨工业大学数学系,哈尔滨工业大学数学系,哈尔滨工业大学数学系 哈尔滨, 150001 ,哈尔滨, 150001 ,哈尔滨, 150001
• 出版日期:2004-02-14 发布日期:2004-02-14

### TH-STABILITY OF θ-METHOD FOR SECOND ORDER DELAY DIFFERENTIAL EQUATION

1. Xu Yang Zhao Jingjun Liu Mingzhu (Department of Mathematics, Harbin Institute of Technology, Harbin, 150001)
• Online:2004-02-14 Published:2004-02-14
1.介 绍 近几年来,一些文章致力于二阶常微分方程数值方法的构造[1,2],但是关于二阶延迟微分方程数值方法的稳定性分析,目前还不多见.据我们所知,只有文献[3]考虑了这类方程可约线性多步法的稳定性.实际上,此类方程在脉冲理论的研究中有着广泛的应用[4].
This paper is concerned with the TH-stability of second order delay differential equation. A sufficient condition such that the system is asymptotically stable is derived. Furthermore, a sufficient condition is obtained for the linear 0-method to be TH-stable. Finally, the plot of stability region for the particular case is presented.
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 [1] M.M. Chawla, A new class of explicit two-step fourth order methods for y" = f(t, y) withextended intervals of periodicity, J. Comput. Appl. Math., 14 (1986) , 467-470． [2] C. Burnton, R. Scherer, Gauss-Runge-Kutta-Nystrom methods, BIT, 38 (1998) , 12-21． [3] B. Cahlon, On the stability of Volterra integral equations with a lagging argument, BIT,35 (1995) , 19-29． [4] D. Morugim, Impulsive Structures with Delayed Feedback, Moscow, 1961． [5] Y.K. Liu, Stability analysis of θ-methods for neutral functional-differential equations, Nu-mer. Math., 70 (1995) , 473-485． [6] J.M. Bownds, J.M. Cushing and R. Schutte, Existence, uniqueness and extendibility ofsolutions of Volterra integral systems with multiple variable lags, Funkcial, Ekvac, 19(1976) , 101-111． [7] R. Bellman, K.L. Cooke, Differential-Difference Equations, Academic Press, New York,1963．
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