A numerical verification method for a periodic solution of a delay differential equation

Teruya Minamoto; Mitsuhiro T. Nakao

doi:10.1016/j.cam.2010.07.018

A numerical verification method for a periodic solution of a delay differential equation

Teruya Minamoto^*, Mitsuhiro T. Nakao

^*Corresponding author for this work

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

14 Citations (Scopus)

Abstract

We describe a numerical method with guaranteed accuracy to enclose a periodic solution for a system of delay differential equations. Using a certain system of equations corresponding to the original system, we derive sufficient conditions for the existence of the solution, the satisfaction of which can be verified computationally. We describe the verification procedure in detail and give a numerical example.

Original language	English
Pages (from-to)	870-878
Number of pages	9
Journal	Journal of Computational and Applied Mathematics
Volume	235
Issue number	3
DOIs	https://doi.org/10.1016/j.cam.2010.07.018
Publication status	Published - 2010 Dec 1
Externally published	Yes

Keywords

Delay differential equation
Delayed feedback control
Numerical computation with guaranteed accuracy
Rssler system

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

Access to Document

10.1016/j.cam.2010.07.018

Cite this

@article{4c26bb75403e45209a825392630f0fd8,

title = "A numerical verification method for a periodic solution of a delay differential equation",

abstract = "We describe a numerical method with guaranteed accuracy to enclose a periodic solution for a system of delay differential equations. Using a certain system of equations corresponding to the original system, we derive sufficient conditions for the existence of the solution, the satisfaction of which can be verified computationally. We describe the verification procedure in detail and give a numerical example.",

keywords = "Delay differential equation, Delayed feedback control, Numerical computation with guaranteed accuracy, Rssler system",

author = "Teruya Minamoto and Nakao, {Mitsuhiro T.}",

year = "2010",

month = dec,

day = "1",

doi = "10.1016/j.cam.2010.07.018",

language = "English",

volume = "235",

pages = "870--878",

journal = "Journal of Computational and Applied Mathematics",

issn = "0377-0427",

publisher = "Elsevier",

number = "3",

}

TY - JOUR

T1 - A numerical verification method for a periodic solution of a delay differential equation

AU - Minamoto, Teruya

AU - Nakao, Mitsuhiro T.

PY - 2010/12/1

Y1 - 2010/12/1

N2 - We describe a numerical method with guaranteed accuracy to enclose a periodic solution for a system of delay differential equations. Using a certain system of equations corresponding to the original system, we derive sufficient conditions for the existence of the solution, the satisfaction of which can be verified computationally. We describe the verification procedure in detail and give a numerical example.

AB - We describe a numerical method with guaranteed accuracy to enclose a periodic solution for a system of delay differential equations. Using a certain system of equations corresponding to the original system, we derive sufficient conditions for the existence of the solution, the satisfaction of which can be verified computationally. We describe the verification procedure in detail and give a numerical example.

KW - Delay differential equation

KW - Delayed feedback control

KW - Numerical computation with guaranteed accuracy

KW - Rssler system

UR - http://www.scopus.com/inward/record.url?scp=77957892615&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77957892615&partnerID=8YFLogxK

U2 - 10.1016/j.cam.2010.07.018

DO - 10.1016/j.cam.2010.07.018

M3 - Article

AN - SCOPUS:77957892615

SN - 0377-0427

VL - 235

SP - 870

EP - 878

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

IS - 3

ER -

A numerical verification method for a periodic solution of a delay differential equation

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this