| 多延迟中立型方程Runge-Kutta方法的NGPG-稳定性 |
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| 引用本文： | 曹婉容,赵景军. 多延迟中立型方程Runge-Kutta方法的NGPG-稳定性[J]. 系统仿真学报, 2007, 19(12): 2698-2700,2705 |
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| 作者姓名： | 曹婉容 赵景军 |
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| 作者单位： | 1. 东南大学数学系,江苏,南京,210096
2. 哈尔滨工业大学数学系,黑龙江,哈尔滨,150001 |
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| 摘 要： | 讨论了多延迟中立型微分方程解析解及由隐式Runge-Kutta方法应用于方程得到的数值解的稳定性.给出了方程解析解渐近稳定的一个充分条件.在此基础上将隐式Runge-Kutta方法应用于方程,证明了数值解NGPG-稳定的充分必要条件为隐式Runge-Kutta方法是A-稳定的.
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| 关 键 词： | 中立型微分方程 多延迟项 隐式Runge-Kutta方法 数值解 NGPG-稳定 |
| 文章编号： | 1004-731X（2007）12-2698-03 |
| 收稿时间： | 2006-05-08 |
| 修稿时间： | 2006-05-082006-09-30 |
NGPG-Stability of Runge-Kutta Methods for Neutral Equations with Multiple Delays |
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| CAO Wan-rong,ZHAO Jing-jun. NGPG-Stability of Runge-Kutta Methods for Neutral Equations with Multiple Delays[J]. Journal of System Simulation, 2007, 19(12): 2698-2700,2705 |
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| Authors: | CAO Wan-rong ZHAO Jing-jun |
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| Affiliation: | 1 .Department of Mathematics, Southeast University, Nanjing 210096, China; 2.Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China |
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| Abstract: | The stability of exact solutions and numerical solutions produced by implicit Runge-Kutta methods for system of neutral differential equations with multiple delays was considered. A sufficient condition for asymptotic stability of exact solutions was established. The implicit Runge-Kutta methods were applied to the system and it is proved that numerical solutions are NGP~-stable if and only if the numerical methods are A- stable. |
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| Keywords: | neutral differential equations multiple delays implicit Runge-Kutta methods numerical solutions NGPG- stability |
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