| 比例延迟微分方程组Rosenbrock方法的渐近稳定性 |
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| 引用本文： | 刘建国,甘四清. 比例延迟微分方程组Rosenbrock方法的渐近稳定性[J]. 系统仿真学报, 2006, 18(12): 3365-3368 |
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| 作者姓名： | 刘建国 甘四清 |
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| 作者单位： | 1. 怀化学院数学与应用数学系,怀化,418008;中南大学数学科学与计算技术学院,长沙,410075
2. 中南大学数学科学与计算技术学院,长沙,410075 |
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| 摘 要： | 讨论用一类变步长Rosenbrock方法求解线性比例延迟微分方程组的渐近稳定性,证明了在无穷远点严格稳定的变步长Rosenbrock方法能够保持原线性系统的渐近稳定性。数值试验进一步验证了算法的理论分析的正确性。
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| 关 键 词： | 线性比例延迟微分方程组 Rosenbrock方法 渐近稳定性 变步长 |
| 文章编号： | 1004-731X（2006）12-3365-04 |
| 收稿时间： | 2005-09-10 |
| 修稿时间： | 2005-11-28 |
Asymptotic Stability of Rosenbrock Methods for System of Pantograph Equation |
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| LIU Jian-guo,GAN Si-qing. Asymptotic Stability of Rosenbrock Methods for System of Pantograph Equation[J]. Journal of System Simulation, 2006, 18(12): 3365-3368 |
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| Authors: | LIU Jian-guo GAN Si-qing |
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| Affiliation: | 1.Department of Mathematics and Applied Mathematics, Huaihua College, Huaihua 418008, China; 2.School of Mathematical Science and Computing Technology, Central South University, Changsha 410075, China |
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| Abstract: | The asymptotic stability of Rosenbrock methods with variable stepsize for the linear system of pantograph equation was discussed, and it is shown that strictly stable at infinity Rosenbrock method with variable stepsize can preserve the asymptotic stability of underlying linear system. Numerical experiment further confirms the theoretical results of numerical analysis. |
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| Keywords: | linear system of pantograph equation Rosenbrock methods asymptotic stability variable stepsize |
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