Stability analysis of numerical methods for linear neutral Volterra delay-integro-differential system

J. J. Zhao; Y. Xu; M. Z. Liu

doi:10.1016/j.amc.2004.08.003

Stability analysis of numerical methods for linear neutral Volterra delay-integro-differential system

J. J. Zhao
, Y. Xu^*
, M. Z. Liu

^*Corresponding author for this work

School of Mathematics

Harbin Institute of Technology

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

40 Scopus citations

Abstract

This paper is concerned with the stability of numerical methods for linear neutral Volterra delay-integro-differential system. A sufficient condition such that the system is asymptotically stable is derived. Furthermore, it is proved that every linear θ-method with θ ∈ (1/2, 1] and A-stable BDF method preserve the delay-independent stability of its exact solutions. Finally, the numerical experiments are given to demonstrate the conclusions.

Original language	English
Pages (from-to)	1062-1079
Number of pages	18
Journal	Applied Mathematics and Computation
Volume	167
Issue number	2
DOIs	https://doi.org/10.1016/j.amc.2004.08.003
State	Published - 15 Aug 2005

Keywords

Delay integro-differential equations
Numerical methods
Stability

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title = "Stability analysis of numerical methods for linear neutral Volterra delay-integro-differential system",

abstract = "This paper is concerned with the stability of numerical methods for linear neutral Volterra delay-integro-differential system. A sufficient condition such that the system is asymptotically stable is derived. Furthermore, it is proved that every linear θ-method with θ ∈ (1/2, 1] and A-stable BDF method preserve the delay-independent stability of its exact solutions. Finally, the numerical experiments are given to demonstrate the conclusions.",

keywords = "Delay integro-differential equations, Numerical methods, Stability",

author = "Zhao, \{J. J.\} and Y. Xu and Liu, \{M. Z.\}",

year = "2005",

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AU - Zhao, J. J.

AU - Xu, Y.

AU - Liu, M. Z.

PY - 2005/8/15

Y1 - 2005/8/15

N2 - This paper is concerned with the stability of numerical methods for linear neutral Volterra delay-integro-differential system. A sufficient condition such that the system is asymptotically stable is derived. Furthermore, it is proved that every linear θ-method with θ ∈ (1/2, 1] and A-stable BDF method preserve the delay-independent stability of its exact solutions. Finally, the numerical experiments are given to demonstrate the conclusions.

AB - This paper is concerned with the stability of numerical methods for linear neutral Volterra delay-integro-differential system. A sufficient condition such that the system is asymptotically stable is derived. Furthermore, it is proved that every linear θ-method with θ ∈ (1/2, 1] and A-stable BDF method preserve the delay-independent stability of its exact solutions. Finally, the numerical experiments are given to demonstrate the conclusions.

KW - Delay integro-differential equations

KW - Numerical methods

KW - Stability

UR - https://www.scopus.com/pages/publications/25144525618

U2 - 10.1016/j.amc.2004.08.003

DO - 10.1016/j.amc.2004.08.003

M3 - 文章

AN - SCOPUS:25144525618

SN - 0096-3003

VL - 167

SP - 1062

EP - 1079

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

IS - 2

ER -

Stability analysis of numerical methods for linear neutral Volterra delay-integro-differential system

Abstract

Keywords

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