| 块θ-方法的PL_m-稳定性 |
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| 引用本文： | 谭秀丽,李顺道,项家祥,丛玉豪.块θ-方法的PL_m-稳定性[J].上海师范大学学报(自然科学版),2007,36(3):6-11. |
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| 作者姓名： | 谭秀丽 李顺道 项家祥 丛玉豪 |
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| 作者单位： | 上海师范大学,数理信息学院,上海,200234 |
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| 基金项目： | 上海市教委资助项目;上海市科委资助项目;国家自然科学基金;上海市教委资助项目 |
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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，分析了块θ-方法求解多延迟微分方程的Pm-稳定性和兕。一稳定性的条件，证明了块θ-方法Pm-稳定的充要条件是1／2≤0≤1，块θ-方法PLm-稳定的充要条件是θ=1．
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| 关 键 词： | 延迟微分方程 块θ-方法 数值稳定性 block θ- method |
| 文章编号： | 1000-5137（2007）03-0006-06 |
| 修稿时间： | 2007-04-12 |
The PLm -stability of the Block θ-method |
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| TAN Xiu-li,LI Shun-dao,XIANG Jia-xiang,CONG Yu-hao.The PLm -stability of the Block θ-method[J].Journal of Shanghai Normal University(Natural Sciences),2007,36(3):6-11. |
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| Authors: | TAN Xiu-li LI Shun-dao XIANG Jia-xiang CONG Yu-hao |
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| Institution: | College of Mathematics and Sciences, Shanghai Normal University, Shanghai 200234, China |
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| Abstract: | The stability behavior of the numerical solution of delay differential equations with many delays is studied. The conditions of the Pm -stability and the PLm -stability of the block θ- method for delay differential equations with many delays are discussed. It is shown that the block θ- method is Pm -stable if and only if 1/2≤θ≤1, the block θ- method is PLm- stable if and only if θ = 1. |
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| Keywords: | delay differential equation numerical stability |
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