| RK-方法求解广义滞时微分方程的GPL-稳定性 |
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| 引用本文： | 丛玉豪,张媛颖,项家祥.RK-方法求解广义滞时微分方程的GPL-稳定性[J].系统仿真学报,2005,17(3):587-589,594. |
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| 作者姓名： | 丛玉豪 张媛颖 项家祥 |
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| 作者单位： | 1. 上海师范大学数学系,桂林路100号,上海,200234;上海高校计算科学E-研究院,桂林路100号,上海,200234
2. 上海师范大学数学系,桂林路100号,上海,200234 |
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| 基金项目： | the National Nature Science Foundation (10171067)，E-Institutes of Shanghai Municipal Education Commission (E03004)，Shanghai Municipal Education Commission (04DB07)，Shanghai Science and Technology Committee (03QA14036)，The Special Funds for Ma |
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| 摘 要： | 讨论了用隐式Runge-Kutta方法求解广义滞时微分方程的数值稳定性，分析了用隐式Runge-Kutta方法求解线性模型方程的GPL-稳定性，证明了隐式Runge-Kutta方法是GPL稳定的，当且仅当它是L-稳定的。
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| 关 键 词： | 广义滞时微分方程 GPL-稳定性 隐式Runge-Kutta方法 L-稳定性 |
The GPL-stability of Runge-Kutta Methods for Generalized Delay Differential System |
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| CONG Yu-hao,ZHANG Yuan-ying,XIANG Jia-xiang.The GPL-stability of Runge-Kutta Methods for Generalized Delay Differential System[J].Journal of System Simulation,2005,17(3):587-589,594. |
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| Authors: | CONG Yu-hao ZHANG Yuan-ying XIANG Jia-xiang |
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| Institution: | CONG Yu-hao1,2,ZHANG Yuan-ying1,XIANG Jia-xiang1 |
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| Abstract: | It is discussed the asymptotic stability analysis of the IRK-method for the numerical solution of generalized delay differential equations. The GPL-stability behavior of IRK-method is analyzed for the solutions of the system of linear test equations. It is shown that the IRK-method is GPL-stable if and only if it is L-stable. |
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| Keywords: | generalized delay differential equation GPL-stability implicit Runge-Kutta method L-stability |
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