| 一类二阶延迟微分方程梯形方法的延迟依赖稳定性分析 |
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| 引用本文： | 黄乘明,李文皓. 一类二阶延迟微分方程梯形方法的延迟依赖稳定性分析[J]. 计算数学, 2007, 29(2): 155-162 |
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| 作者姓名： | 黄乘明 李文皓 |
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| 作者单位： | 华中科技大学数学系,武汉,430074;华中科技大学数学系,武汉,430074 |
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| 基金项目： | 国家自然科学基金 , 教育部跨世纪优秀人才培养计划 , 教育部留学回国人员科研启动基金 |
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| 摘 要： | 本文涉及一类二阶延迟微分方程数值方法的稳定性研究．通过运用边界轨迹法,分析了梯形方法的延迟依赖稳定区域并找到其准确边界．随后建立了解析和数值稳定区域的联系并从理论上证明了梯形方法能完全保持模型问题的延迟依赖稳定性．
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| 关 键 词： | 梯形方法 延迟依赖稳定区域 二阶延迟微分方程 |
| 修稿时间： | 2005-12-09 |
DELAY-DEPENDENT STABILITY ANALYSIS OF THE TRAPEZIUM RULE FOR A CLASS OF SECOND ORDER DELAY DIFFERENTIAL EQUATIONS |
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| Huang Chengming,Li Wenhao. DELAY-DEPENDENT STABILITY ANALYSIS OF THE TRAPEZIUM RULE FOR A CLASS OF SECOND ORDER DELAY DIFFERENTIAL EQUATIONS[J]. Mathematica Numerica Sinica, 2007, 29(2): 155-162 |
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| Authors: | Huang Chengming Li Wenhao |
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| Affiliation: | Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074, China |
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| Abstract: | This paper is concerned with the study of the stability of numerical methods for a class of second order delay differential equations. By using the boundary locus method, the delay-dependent stability region of the trapezium rule is analyzed and its boundary is found. Then the relationship between analytical and numerical stability regions is identified and it is proved theoretically that the trapezium rule can completely preserve the delay-dependent stability for the considered set of test problems. |
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| Keywords: | trapezium rule delay-dependent stability second order delay differential equations |
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