[1] Wang Hongshan, Zhang Chengjian,. Stability analysis for nonlinear multi-variabledelay perturbation problems [J]. Journal of Southeast University (English Edition), 2003, 19 (2): 193-196. [doi:10.3969/j.issn.1003-7985.2003.02.020]

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Stability analysis for nonlinear multi-variabledelay perturbation problems()

非线性多变延迟奇异摄动问题的稳定性分析

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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:

19

Issue:

2003 2

Page:

193-196

Research Field:

Mathematics, Physics, Mechanics

Publishing date:

2003-06-30

Info

Title:

Stability analysis for nonlinear multi-variabledelay perturbation problems

非线性多变延迟奇异摄动问题的稳定性分析

Author(s):

Wang Hongshan¹, Zhang Chengjian²

¹Department of Mathematics, Wuhan Institute of Science and Technology, Wuhan 430073, China
²Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074, China

王洪山, 张诚坚

武汉科技学院数学系, 武汉 430073) (华中科技大学数学系, 武汉 430074

Keywords:

multi-variable delay perturbation problems;  Euler method;  stability;  interpolation

多变时滞奇异摄动问题;  Euler方法;  稳定性;  插值

PACS:

O241.3

DOI:

10.3969/j.issn.1003-7985.2003.02.020

Abstract:

This paper discusses the stability of theoretical solutions for nonlinear multi-variable delay perturbation problems(MVDPP)of the form x′(t)=f(x(t), x(t-τ₁(t)), …, x(t-τ_m(t)), y(t), y(t-τ₁(t)), …, y(t-τ_m(t))), and εy′(t)=g(x(t), x(t-τ₁(t)), …, x(t-τ_m(t)), y(t), y(t-τ₁(t)), …, y(t-τ_m(t))), where 0<ε≪1. A sufficient condition of stability for the systems is obtained. Additionally we prove the numerical solutions of the implicit Euler method are stable under this condition.

讨论了形如x′(t)=f(x(t), x(t-τ₁(t)), …, x(t-τ_m(t)), y(t), y(t-τ₁(t)), …, y(t-τ_m(t)))和εy′(t)=g(x(t), x(t-τ₁(t)), …, x(t-τ_m(t)), y(t), y(t-τ₁(t)), …, y(t-τ_m(t)))(0<ε

References:

[1] Gan Siqing, Sun Geng. Error of Runge-Kutta methods for singular perturbation problems with delays [J]. Mathematica Numerica Sinica, 2001, 123(3):343-356.(in Chinese)
[2] Hairer E, Wanner G. Solving ordinary differential equations Ⅱ[M]. Berlin: Springer, 1991.
[3] Buhmann M D, Iserles A. Numerical analysis of delay differential equations with variable delay [J]. Ann Numer Math, 1994, 1(1):133-152.
[4] Torelli L. A sufficient condition for GPN-stability for delay differential equations[J]. Numer Math, 1991, 59(3): 311-320.
[5] Zhang Chengjian, Liao Xiaoxin. Contractivity of Runge-Kutta methods for multidelay differential equations[J]. Acta Mathematica Scientia, 2001, 21(2):252-258.(in Chinese)

Memo

Memo:

Biography: Wang Hongshan(1974—), male, master.

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