Stability analysis of extended block boundary value methods for linear neutral delay integro-differential equations

Jingjun Zhao; Yang Xu; Zheng Gao

doi:10.1080/00207160.2012.738812

Stability analysis of extended block boundary value methods for linear neutral delay integro-differential equations

Jingjun Zhao
, Yang Xu^*
, Zheng Gao

^*Corresponding author for this work

School of Mathematics

Harbin Institute of Technology

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

11 Scopus citations

Abstract

This paper is concerned with the stability of extended block boundary value methods (B₂VMs) for the linear neutral delay integro-differential-algebraic equations (NDIDAEs) and the linear neutral delay integro-differential equations (NDIDEs). It is proved that every A-stable B₂VM can preserve the asymptotic stability of the exact solution of NDIDAEs under some certain conditions. A necessary and sufficient condition of the B₂VMs to be asymptotically stable for NDIDEs is also obtained. A few numerical experiments confirm the expected results.

Original language	English
Pages (from-to)	705-726
Number of pages	22
Journal	International Journal of Computer Mathematics
Volume	90
Issue number	3
DOIs	https://doi.org/10.1080/00207160.2012.738812
State	Published - 2013

Keywords

Asymptotic stability
Block boundary value methods
Delay differential-algebraic equations
Delay integro-differential equations
Reducible quadrature rules

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10.1080/00207160.2012.738812

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title = "Stability analysis of extended block boundary value methods for linear neutral delay integro-differential equations",

abstract = "This paper is concerned with the stability of extended block boundary value methods (B2VMs) for the linear neutral delay integro-differential-algebraic equations (NDIDAEs) and the linear neutral delay integro-differential equations (NDIDEs). It is proved that every A-stable B2VM can preserve the asymptotic stability of the exact solution of NDIDAEs under some certain conditions. A necessary and sufficient condition of the B2VMs to be asymptotically stable for NDIDEs is also obtained. A few numerical experiments confirm the expected results.",

keywords = "Asymptotic stability, Block boundary value methods, Delay differential-algebraic equations, Delay integro-differential equations, Reducible quadrature rules",

author = "Jingjun Zhao and Yang Xu and Zheng Gao",

note = "Publisher Copyright: {\textcopyright} 2013 Taylor \& Francis.",

year = "2013",

doi = "10.1080/00207160.2012.738812",

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T1 - Stability analysis of extended block boundary value methods for linear neutral delay integro-differential equations

AU - Zhao, Jingjun

AU - Xu, Yang

AU - Gao, Zheng

PY - 2013

Y1 - 2013

N2 - This paper is concerned with the stability of extended block boundary value methods (B2VMs) for the linear neutral delay integro-differential-algebraic equations (NDIDAEs) and the linear neutral delay integro-differential equations (NDIDEs). It is proved that every A-stable B2VM can preserve the asymptotic stability of the exact solution of NDIDAEs under some certain conditions. A necessary and sufficient condition of the B2VMs to be asymptotically stable for NDIDEs is also obtained. A few numerical experiments confirm the expected results.

AB - This paper is concerned with the stability of extended block boundary value methods (B2VMs) for the linear neutral delay integro-differential-algebraic equations (NDIDAEs) and the linear neutral delay integro-differential equations (NDIDEs). It is proved that every A-stable B2VM can preserve the asymptotic stability of the exact solution of NDIDAEs under some certain conditions. A necessary and sufficient condition of the B2VMs to be asymptotically stable for NDIDEs is also obtained. A few numerical experiments confirm the expected results.

KW - Asymptotic stability

KW - Block boundary value methods

KW - Delay differential-algebraic equations

KW - Delay integro-differential equations

KW - Reducible quadrature rules

UR - https://www.scopus.com/pages/publications/84869878767

U2 - 10.1080/00207160.2012.738812

DO - 10.1080/00207160.2012.738812

M3 - 文章

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SN - 0020-7160

VL - 90

SP - 705

EP - 726

JO - International Journal of Computer Mathematics

JF - International Journal of Computer Mathematics

IS - 3

ER -

Stability analysis of extended block boundary value methods for linear neutral delay integro-differential equations

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Keywords

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