| 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. |
| 关键词: 延时微分方程组 GPmL-稳定性 Rosenbrock方法 |
| DOI： |
| 分类号: |
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| GPmL-stability of the Rosenbrock methods for the systems of differential equations with many delays |
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LU Zhiwen
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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. |
| Key words: delay differential equation GPmL-stability Rosenbrock method |
