Exponential stability of the exact solutions and the numerical solutions for a class of linear impulsive delay differential equations

G. L. Zhang; M. H. Song; M. Z. Liu

doi:10.1016/j.cam.2015.01.034

Exponential stability of the exact solutions and the numerical solutions for a class of linear impulsive delay differential equations

G. L. Zhang
, M. H. Song^*
, M. Z. Liu

^*Corresponding author for this work

School of Mathematics

Harbin Institute of Technology
Northeastern University China

Research output: Contribution to journal › Article › peer-review

33 Scopus citations

Abstract

This paper is concerned with exponential stability of a class of linear impulsive delay differential equations (IDDEs). Exponential stability of this kind of equations is studied by the properties of delay differential equations (DDEs) without impulsive perturbations. When different delay differential equations (DDEs) without impulsive perturbations are chosen, different sufficient conditions for exponential stability of the linear impulsive delay differential equations (IDDEs) are provided. Numerical methods for this kind of equations are constructed. The convergence and exponential stability of the numerical solutions are studied and some experiments are given.

Original language	English
Pages (from-to)	32-44
Number of pages	13
Journal	Journal of Computational and Applied Mathematics
Volume	285
DOIs	https://doi.org/10.1016/j.cam.2015.01.034
State	Published - Sep 2015

Keywords

Exponentially stable
Impulsive delay differential equation
Runge-Kutta method

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10.1016/j.cam.2015.01.034

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title = "Exponential stability of the exact solutions and the numerical solutions for a class of linear impulsive delay differential equations",

abstract = "This paper is concerned with exponential stability of a class of linear impulsive delay differential equations (IDDEs). Exponential stability of this kind of equations is studied by the properties of delay differential equations (DDEs) without impulsive perturbations. When different delay differential equations (DDEs) without impulsive perturbations are chosen, different sufficient conditions for exponential stability of the linear impulsive delay differential equations (IDDEs) are provided. Numerical methods for this kind of equations are constructed. The convergence and exponential stability of the numerical solutions are studied and some experiments are given.",

keywords = "Exponentially stable, Impulsive delay differential equation, Runge-Kutta method",

author = "Zhang, \{G. L.\} and Song, \{M. H.\} and Liu, \{M. Z.\}",

year = "2015",

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doi = "10.1016/j.cam.2015.01.034",

language = "英语",

volume = "285",

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T1 - Exponential stability of the exact solutions and the numerical solutions for a class of linear impulsive delay differential equations

AU - Zhang, G. L.

AU - Song, M. H.

AU - Liu, M. Z.

PY - 2015/9

Y1 - 2015/9

N2 - This paper is concerned with exponential stability of a class of linear impulsive delay differential equations (IDDEs). Exponential stability of this kind of equations is studied by the properties of delay differential equations (DDEs) without impulsive perturbations. When different delay differential equations (DDEs) without impulsive perturbations are chosen, different sufficient conditions for exponential stability of the linear impulsive delay differential equations (IDDEs) are provided. Numerical methods for this kind of equations are constructed. The convergence and exponential stability of the numerical solutions are studied and some experiments are given.

AB - This paper is concerned with exponential stability of a class of linear impulsive delay differential equations (IDDEs). Exponential stability of this kind of equations is studied by the properties of delay differential equations (DDEs) without impulsive perturbations. When different delay differential equations (DDEs) without impulsive perturbations are chosen, different sufficient conditions for exponential stability of the linear impulsive delay differential equations (IDDEs) are provided. Numerical methods for this kind of equations are constructed. The convergence and exponential stability of the numerical solutions are studied and some experiments are given.

KW - Exponentially stable

KW - Impulsive delay differential equation

KW - Runge-Kutta method

UR - https://www.scopus.com/pages/publications/84923383122

U2 - 10.1016/j.cam.2015.01.034

DO - 10.1016/j.cam.2015.01.034

M3 - 文章

AN - SCOPUS:84923383122

SN - 0377-0427

VL - 285

SP - 32

EP - 44

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

ER -

Exponential stability of the exact solutions and the numerical solutions for a class of linear impulsive delay differential equations

Abstract

Keywords

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