| Rosenbrock方法求解多延时微分方程组的GPmL-稳定性 |
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| 引用本文： | 陆志雯.Rosenbrock方法求解多延时微分方程组的GPmL-稳定性[J].上海师范大学学报(自然科学版),2014,43(2):111-116. |
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| 作者姓名： | 陆志雯 |
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| 作者单位： | 上海理工大学理学院; |
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| 摘 要： | 研究了用Rosenbrock方法求解多延时微分方程组数值解的稳定性.Rosenbrock方法是求解刚性常微分方程的有效方法,基于Lagrange插值,借助于理论解渐近稳定的条件,对于线型方程组模型,分析了Rosenbrock方法的GPmL-稳定性,并证明了用Rosenbrock方法数值求解多延时微分方程组是GPmL-稳定的当且仅当它是L-稳定的.
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| 关 键 词： | 延时微分方程组 GPmL-稳定性 Rosenbrock方法 |
| 收稿时间： | 2013/11/15 0:00:00 |
GPmL-stability of the Rosenbrock methods for the systems of differential equations with many delays |
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| LU Zhiwen.GPmL-stability of the Rosenbrock methods for the systems of differential equations with many delays[J].Journal of Shanghai Normal University(Natural Sciences),2014,43(2):111-116. |
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| Authors: | LU Zhiwen |
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| Institution: | LU Zhiwen;School of Science,University of Shanghai for Science and Technology; |
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| Abstract: | This paper deals with the stability analysis of the Rosenbrock methods for the numerical solutions of the systems of differential equations with many delays. The GPmL-stability behavior of the Rosenbrock methods is analyzed for the solutions of linear test equations. We show that the Rosenbrock methods are GPmL-stable if and only if they are L-stable. |
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| Keywords: | delay differential equation GPmL-stability Rosenbrock method |
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