| 周期时变线性系统的周期精细积分算法 |
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| 引用本文： | 周钢,江琳.周期时变线性系统的周期精细积分算法[J].上海交通大学学报,2005,39(6):1016-1019. |
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| 作者姓名： | 周钢 江琳 |
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| 作者单位： | 上海交通大学,数学系,上海,200240;上海交通大学,数学系,上海,200240 |
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| 基金项目： | 国家自然科学基金资助项目(50376039)，教育部科学技术研究重点资助项目 |
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| 摘 要： | 周期时变线性系统系数矩阵的时变性与不可交换性是其精细积分算法设计中的瓶颈，应用Peano-Baker级数理论：首先在单周期内获得精细转移矩阵，然后利用周期性简化计算，这不仅有效地提高了全时域上的计算精度，而且还能节省较多计算量．本文设计了2个数值算例，与四阶R—K算法的数值解相比较，结果表明，本文建立的周期时变精细积分算法(PTHPD)有明显的优越性。
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| 关 键 词： | 精细积分 转移矩阵 Peano-Baker级数 周期时变线性系统 |
| 文章编号： | 1006-2467(2005)06-1016-04 |
| 修稿时间： | 2004年5月25日 |
A High Precision Direct Integration Method for Periodically Time-Varying Linear System |
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| ZHOU Gang,JIANG Lin.A High Precision Direct Integration Method for Periodically Time-Varying Linear System[J].Journal of Shanghai Jiaotong University,2005,39(6):1016-1019. |
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| Authors: | ZHOU Gang JIANG Lin |
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| Abstract: | The time-varying and incommutable character of the coefficient matrix of periodically time-varying linear systems are the bottleneck of the design for high precision direct integration methods. This paper solved the difficult problem with the theory of Peano-Baker series:first, to get the precise transfer matrix in a single period, then to simplify the computation with the periodicity. This algorithm can not only improve the accuracy of computation in the whole time domain, but also save much computation. Two numerical examples were given, and the results show the periodically time-varying high precision direct integration method(PTHPD) is superior obviously to the fourth-order R-K method. |
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| Keywords: | high precision direct integration transfer matrix Peano-Baker series periodically time-varying linear systems |
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