| 求解延迟微分方程块θ-方法的GPLm-稳定性 |
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| 引用本文： | 丛玉豪,李顺道,谭秀丽. 求解延迟微分方程块θ-方法的GPLm-稳定性[J]. 系统仿真学报, 2007, 19(17) |
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| 作者姓名： | 丛玉豪 李顺道 谭秀丽 |
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| 作者单位： | 1. 上海师范大学数学系,上海,200234;上海高校计算科学E-研究院,上海,200234
2. 上海师范大学数学系,上海,200234 |
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| 基金项目： | 上海市教委资助项目;上海市教委资助项目;上海市科委资助项目 |
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| 摘 要： | 讨论了带有多个滞时量的延时微分方程的数值稳定性,分析了用块θ–方法求解多延迟微分方程GPm–稳定和GPLm–稳定的条件,基于Lagrange插值,证明了块θ–方法GPm–稳定的充分必要条件是方法是A-稳定的,块θ–方法GPLm–稳定的充分必要条件是θ=1。
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| 关 键 词： | 延时微分方程 数值稳定性 块θ-方法 L-稳定性 block θ-method |
GPLm-Stability of Block θ-method for Delay Differential Equation |
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| CONG Yu-hao,LI Shun-dao,TAN Xiu-li. GPLm-Stability of Block θ-method for Delay Differential Equation[J]. Journal of System Simulation, 2007, 19(17) |
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| Authors: | CONG Yu-hao LI Shun-dao TAN Xiu-li |
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| Abstract: | The stability behavior of numerical solution for delay differential equations with many delays was studied. The conditions of GPmstability and GPLmstability of blockθ-method for delay differential equations with many delays were discussed. By Lagrange Interpolation, it is shown that blockθ-method is GPm-stable if and only if it is A-stable, block-θ method is GPLm-stable if and only if θ=1. |
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| Keywords: | delay differential equation numerical stability L-stability |
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