Delay-dependent stability of linear multistep methods for differential systems with distributed delays

doi:10.1007/s10483-018-2392-9

Applied Mathematics and Mechanics (English Edition) ›› 2018, Vol. 39 ›› Issue (12): 1837-1844.doi: https://doi.org/10.1007/s10483-018-2392-9

Delay-dependent stability of linear multistep methods for differential systems with distributed delays

Yanpei WANG¹, Yuhao CONG^1,2, Guangda HU¹

1. Department of Mathematics, College of Sciences, Shanghai University, Shanghai 200444, China;
2. Shanghai Customs College, Shanghai 201204, China

收稿日期:2018-03-16 修回日期:2018-04-04 出版日期:2018-12-01 发布日期:2018-12-01
通讯作者: Yuhao CONG E-mail:yhcong@shu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (No. 11471217)

Delay-dependent stability of linear multistep methods for differential systems with distributed delays

Yanpei WANG¹, Yuhao CONG^1,2, Guangda HU¹

1. Department of Mathematics, College of Sciences, Shanghai University, Shanghai 200444, China;
2. Shanghai Customs College, Shanghai 201204, China

Received:2018-03-16 Revised:2018-04-04 Online:2018-12-01 Published:2018-12-01
Contact: Yuhao CONG E-mail:yhcong@shu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (No. 11471217)

摘要/Abstract

摘要： This paper deals with the stability of linear multistep methods for multidimensional differential systems with distributed delays. The delay-dependent stability of linear multistep methods with compound quadrature rules is studied. Several new sufficient criteria of delay-dependent stability are obtained by means of the argument principle. An algorithm is provided to check delay-dependent stability. An example that illustrates the effectiveness of the derived theoretical results is given.

关键词: Newton-Raphson method, penalty function method, nonlineareffect, drill string, differential system with distributed delays, delay-dependent stability, linear multistep method, argument principle

Abstract: This paper deals with the stability of linear multistep methods for multidimensional differential systems with distributed delays. The delay-dependent stability of linear multistep methods with compound quadrature rules is studied. Several new sufficient criteria of delay-dependent stability are obtained by means of the argument principle. An algorithm is provided to check delay-dependent stability. An example that illustrates the effectiveness of the derived theoretical results is given.

Key words: Newton-Raphson method, penalty function method, nonlineareffect, drill string, delay-dependent stability, linear multistep method, argument principle, differential system with distributed delays

中图分类号:

Yanpei WANG, Yuhao CONG, Guangda HU. Delay-dependent stability of linear multistep methods for differential systems with distributed delays[J]. Applied Mathematics and Mechanics (English Edition), 2018, 39(12): 1837-1844.

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Delay-dependent stability of linear multistep methods for differential systems with distributed delays

Delay-dependent stability of linear multistep methods for differential systems with distributed delays

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