ℋ-stability of linear θ-method with general variable stepsize for system of pantograph equations with two delay terms

Yang Xu; Ming Zhu Liu

doi:10.1016/j.amc.2003.06.008

ℋ-stability of linear θ-method with general variable stepsize for system of pantograph equations with two delay terms

Yang Xu^*
, Ming Zhu Liu

^*Corresponding author for this work

School of Mathematics

Harbin Institute of Technology

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

6 Scopus citations

Abstract

This paper deals with ℋ-stability of the linear θ-method with a general variable stepsize for the system of pantograph equations with two delay terms. A sufficient condition such that the system of pantograph equations is asymptotically stable is derived. Furthermore, when the linear θ-method with a general variable stepsize is applied to this system, it is shown that the linear θ-method is ℋ-stable if and only if 1/2<θ≤1.

Original language	English
Pages (from-to)	817-829
Number of pages	13
Journal	Applied Mathematics and Computation
Volume	156
Issue number	3
DOIs	https://doi.org/10.1016/j.amc.2003.06.008
State	Published - 15 Sep 2004

Keywords

Delay differential equations
Infinite lag
Numerical solution
Stability
θ-method

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10.1016/j.amc.2003.06.008

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title = "ℋ-stability of linear θ-method with general variable stepsize for system of pantograph equations with two delay terms",

abstract = "This paper deals with ℋ-stability of the linear θ-method with a general variable stepsize for the system of pantograph equations with two delay terms. A sufficient condition such that the system of pantograph equations is asymptotically stable is derived. Furthermore, when the linear θ-method with a general variable stepsize is applied to this system, it is shown that the linear θ-method is ℋ-stable if and only if 1/2<θ≤1.",

keywords = "Delay differential equations, Infinite lag, Numerical solution, Stability, θ-method",

author = "Yang Xu and Liu, \{Ming Zhu\}",

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T1 - ℋ-stability of linear θ-method with general variable stepsize for system of pantograph equations with two delay terms

AU - Xu, Yang

AU - Liu, Ming Zhu

PY - 2004/9/15

Y1 - 2004/9/15

N2 - This paper deals with ℋ-stability of the linear θ-method with a general variable stepsize for the system of pantograph equations with two delay terms. A sufficient condition such that the system of pantograph equations is asymptotically stable is derived. Furthermore, when the linear θ-method with a general variable stepsize is applied to this system, it is shown that the linear θ-method is ℋ-stable if and only if 1/2<θ≤1.

AB - This paper deals with ℋ-stability of the linear θ-method with a general variable stepsize for the system of pantograph equations with two delay terms. A sufficient condition such that the system of pantograph equations is asymptotically stable is derived. Furthermore, when the linear θ-method with a general variable stepsize is applied to this system, it is shown that the linear θ-method is ℋ-stable if and only if 1/2<θ≤1.

KW - Delay differential equations

KW - Infinite lag

KW - Numerical solution

KW - Stability

KW - θ-method

UR - https://www.scopus.com/pages/publications/4344688733

U2 - 10.1016/j.amc.2003.06.008

DO - 10.1016/j.amc.2003.06.008

M3 - 文章

AN - SCOPUS:4344688733

SN - 0096-3003

VL - 156

SP - 817

EP - 829

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

IS - 3

ER -

ℋ-stability of linear θ-method with general variable stepsize for system of pantograph equations with two delay terms

Abstract

Keywords

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