| 延迟积分微分方程线性多步方法的稳定性分析 |
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| 引用本文： | 刘建国,姚金然,卢菁菁. 延迟积分微分方程线性多步方法的稳定性分析[J]. 数学理论与应用, 2008, 28(4): 45-48 |
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| 作者姓名： | 刘建国 姚金然 卢菁菁 |
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| 作者单位： | [1]中南大学数学科学与计算技术学院,长沙410075 [2]黄山学院数学系,黄山245041 |
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| 摘 要： | 考虑带常延迟的延迟积分微分方程线性系统零解的渐近稳定性，本文采用拉格朗日插值的线性多步方法，探讨了系统数值方法的线性稳定性。证明了所有A-稳定且强零-稳定的Pouzet型线性多步方法能够保持原线性系统的延迟不依赖稳定性。
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| 关 键 词： | 延迟积分微分方程 Pouzet型线性多步法 拉格朗日插值 渐近稳定性 |
Stability Analysis of Linear Multistep Methods for Delay Integro-Differential Equatioins |
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| Liu Jianguo Yao Jinran Lu Jingjing. Stability Analysis of Linear Multistep Methods for Delay Integro-Differential Equatioins[J]. Mathematical Theory and Applications, 2008, 28(4): 45-48 |
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| Authors: | Liu Jianguo Yao Jinran Lu Jingjing |
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| Affiliation: | Liu Jianguo1 Yao Jinran2 Lu Jingjing1(1.School of Mathematical Science , Computing Technology,Central South University,Changsha,410075)(2.Department of Mathematics,Huangshan College,Huangshan,245041) |
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| Abstract: | For a linear system of delay integro-differential equations with a constant delay whose zero solution is asymptotically stable,this paper deals with the linear stability of numerical methods for the system.The adaptation of linear multistep methods with a Lagrange interpolation is considered.It is proven that every A-stable,strongly zero-stable linear multistep methods of Pouzet type can preserve the delay-independent stability of the underlying linear systems. |
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| Keywords: | Delay integro-differential equations Linear multistep methods of Pouzet type Lagrange interpolation Asymptotic stability |
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