中立型时滞微分方程 Rosenbrock 方法的弱时滞相关稳定性

doi:10.12066/j.issn.1007-2861.2115

上海大学学报(自然科学版) ›› 2021, Vol. 27 ›› Issue (1): 208-217.doi: 10.12066/j.issn.1007-2861.2115

中立型时滞微分方程 Rosenbrock 方法的弱时滞相关稳定性

张明坤¹, 王艳沛¹^,²(), 赵欢欢¹

1.上海大学理学院, 上海 200444
2.郑州航空工业管理学院数学学院, 郑州 450046

收稿日期:2018-12-11 出版日期:2021-02-28 发布日期:2021-02-28
通讯作者: 王艳沛 E-mail:wangyanpei@163.com
作者简介:王艳沛(1988---), 女, 博士, 研究方向为微分方程数值解. E-mail: wangyanpei@163.com.
基金资助:
国家自然科学基金资助项目(11471217)

Weak delay-dependent stability of Rosenbrock methods for neutral delay differential equations

ZHANG Mingkun¹, WANG Yanpei¹^,²(), ZHAO Huanhuan¹

1. College of Sciences, Shanghai University, Shanghai 200444, China
2. School of Mathematics, ZhengzhouUniversity of Aeronautics, Zhengzhou 450046, China

Received:2018-12-11 Online:2021-02-28 Published:2021-02-28
Contact: WANG Yanpei E-mail:wangyanpei@163.com

摘要/Abstract

摘要：

在中立型时滞微分方程存在时滞相关渐近稳定解的条件下, 研究了中立型时滞微分方程的 Rosenbrock 方法的弱时滞相关稳定性. 基于辐角原理, 给出了 Rosenbrock 方法的弱时滞渐近稳定性的充分条件, 并通过数值例子验证理论结果的有效性.

关键词: 中立型时滞微分方程, Rosenbrock 方法, 辐角原理, 弱时滞相关稳定性

Abstract:

The weak delay-dependent stability of the Rosenbrock methods for neutral delay differential equations is studied under the condition that the equations are delay-dependent asymptotically stable. Based on the argument principle, a sufficient condition for the weak delay asymptotic stability of Rosenbrock methods is given. Finally, numerical examples are provided to verify the effectiveness of the theoretical results.

Key words: neutral delay differential equation, Rosenbrock method, argument principle, weak delay-dependent stability

中图分类号:

O241.8

张明坤, 王艳沛, 赵欢欢. 中立型时滞微分方程 Rosenbrock 方法的弱时滞相关稳定性[J]. 上海大学学报(自然科学版), 2021, 27(1): 208-217.

ZHANG Mingkun, WANG Yanpei, ZHAO Huanhuan. Weak delay-dependent stability of Rosenbrock methods for neutral delay differential equations[J]. Journal of Shanghai University（Natural Science Edition）, 2021, 27(1): 208-217.

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中立型时滞微分方程 Rosenbrock 方法的弱时滞相关稳定性

Weak delay-dependent stability of Rosenbrock methods for neutral delay differential equations

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