Publication result detail

Exact versus discretized stability regions for a linear delay differential equation

ČERMÁK, J.; JÁNSKÝ, J.; NECHVÁTAL, L.

Original Title

Exact versus discretized stability regions for a linear delay differential equation

English Title

Exact versus discretized stability regions for a linear delay differential equation

Type

WoS Article

Original Abstract

The paper introduces a system of necessary and sufficient stability conditions for a four- term linear delay difference equation with complex coefficients. These conditions are de- rived explicitly with respect to the time lag and can be viewed as a direct discrete coun- terpart to the existing stability results for the underlying delay differential equation. As a main proof tool, the boundary locus technique combined with some special results of the polynomial theory is employed. Since the studied difference equation serves as a θ - method discretization of its continuous pattern, several problems of numerical stability are discussed as well.

English abstract

The paper introduces a system of necessary and sufficient stability conditions for a four- term linear delay difference equation with complex coefficients. These conditions are de- rived explicitly with respect to the time lag and can be viewed as a direct discrete coun- terpart to the existing stability results for the underlying delay differential equation. As a main proof tool, the boundary locus technique combined with some special results of the polynomial theory is employed. Since the studied difference equation serves as a θ - method discretization of its continuous pattern, several problems of numerical stability are discussed as well.

Keywords

Linear delay difference equation; Linear delay differential equation; θ -method discretization; Exact and numerical stability

Key words in English

Linear delay difference equation; Linear delay differential equation; θ -method discretization; Exact and numerical stability

Authors

ČERMÁK, J.; JÁNSKÝ, J.; NECHVÁTAL, L.

RIV year

2019

Released

15.04.2019

Publisher

Elsevier Science Inc.

Location

New York, USA

ISBN

0096-3003

Periodical

APPLIED MATHEMATICS AND COMPUTATION

Volume

347

Number

1

State

United States of America

Pages from

712

Pages to

722

Pages count

11

URL

https://www.sciencedirect.com/science/article/pii/S0096300318310002

BibTex

@article{BUT155747,
  author="Jan {Čermák} and Jiří {Jánský} and Luděk {Nechvátal}",
  title="Exact versus discretized stability regions for a linear delay differential equation",
  journal="APPLIED MATHEMATICS AND COMPUTATION",
  year="2019",
  volume="347",
  number="1",
  pages="712--722",
  doi="10.1016/j.amc.2018.11.026",
  issn="0096-3003",
  url="https://www.sciencedirect.com/science/article/pii/S0096300318310002"
}