| 延迟系统的并行BDF算法及其稳定性分析 |
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| 引用本文： | 侯战友,刘伟丰,黄枝姣,蒋洪波.延迟系统的并行BDF算法及其稳定性分析[J].华中科技大学学报(自然科学版),2001,29(6):114-116. |
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| 作者姓名： | 侯战友 刘伟丰 黄枝姣 蒋洪波 |
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| 作者单位： | 华中科技大学数学系 |
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| 基金项目： | 国家自然科学基金资助项目 (6 99740 18) |
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| 摘 要： | 以显式BDF方法为预估式，以隐式BDF方法为校正式构造了一类求解延迟系统的并行BDF算法，探讨了算法的稳定性，得到了算法渐进稳定的一个充分条件，导出了该算法的稳定性是由相应的常微系统（ODEs)的方法的稳定性控制的，理论分析和数值试验表明，算法对线性和非线性问题均有良好的效果。
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| 关 键 词： | 并行BDF算法 延迟系统 稳定性 显式BDF方法 隐式BDF方法 预估式 |
| 文章编号： | 1000-8616(2001)06-0114-03 |
| 修稿时间： | 2000年12月14 |
Parallel BDF Algorithms for Delay Systems with Stability Analysis |
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| Hou Zhanyou Liu Weifeng Huang Zhijiao Jiang Hongbo Postgraduate, Dept. of Math.,HUST,Wuhan ,China..Parallel BDF Algorithms for Delay Systems with Stability Analysis[J].JOURNAL OF HUAZHONG UNIVERSITY OF SCIENCE AND TECHNOLOGY.NATURE SCIENCE,2001,29(6):114-116. |
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| Authors: | Hou Zhanyou Liu Weifeng Huang Zhijiao Jiang Hongbo Postgraduate Dept of Math HUST Wuhan China |
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| Institution: | Hou Zhanyou Liu Weifeng Huang Zhijiao Jiang Hongbo Postgraduate, Dept. of Math.,HUST,Wuhan 430074,China. |
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| Abstract: | This paper constructs a class of parallel BDF algorithms for the systems of delay differential equations with explicit BDF methods as predictor and implicit BDF methods as corrector. In the paper the stability analysis is discussed, and a sufficient condition under which the systems of delay differential equations are asymptotically stable is derived. It is easily inferred that the stability of the algorithm is controlled by the stability of the corresponding ordinary differential equations. Some results of numerical tests are also presented. From theoretical analysis and numerical tests the conclusion can be drawn that the algorithm is not only for linear problems, but also for nonlinear problems. |
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| Keywords: | parallel algorithms BDF methods delay system stability |
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