Small delay inertial manifolds under numerics: A numerical structural stability result

Gyula Farkas; George R. Sell

doi:10.1023/A:1016335115301

Small delay inertial manifolds under numerics: A numerical structural stability result

Gyula Farkas, George R. Sell

School of Mathematics

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

5 Scopus citations

Abstract

In this paper we formulate a numerical structural stability result for delay equations with small delay under Euler discretization. The main ingredients of our approach are the existence and smoothness of small delay inertial manifolds, the C¹-closeness of the small delay inertial manifolds and their numerical approximation and M.-C. Li's recent result on numerical structural stability of ordinary differential equations under the Euler method.

Original language	English (US)
Pages (from-to)	549-588
Number of pages	40
Journal	Journal of Dynamics and Differential Equations
Volume	14
Issue number	3
DOIs	https://doi.org/10.1023/A:1016335115301
State	Published - 2002

Bibliographical note

Funding Information:
Supported by DAAD project 323-PPP, Qualitative Theory of Numerical Methods for Evolution Equations in Infinite Dimensions. This work was done while the author was a visitor at the University of Bielefeld. The author would like to thank Prof. W.-J. Beyn for the stimulating discussions. The author is also grateful to the referee for his/her valuable comments.

Keywords

C -estimates
Delay equations
Euler method
Numerical structural stability
Small delay inertial manifolds
Smoothness

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10.1023/A:1016335115301

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title = "Small delay inertial manifolds under numerics: A numerical structural stability result",

abstract = "In this paper we formulate a numerical structural stability result for delay equations with small delay under Euler discretization. The main ingredients of our approach are the existence and smoothness of small delay inertial manifolds, the C1-closeness of the small delay inertial manifolds and their numerical approximation and M.-C. Li's recent result on numerical structural stability of ordinary differential equations under the Euler method.",

keywords = "C -estimates, Delay equations, Euler method, Numerical structural stability, Small delay inertial manifolds, Smoothness",

author = "Gyula Farkas and Sell, {George R.}",

note = "Funding Information: Supported by DAAD project 323-PPP, Qualitative Theory of Numerical Methods for Evolution Equations in Infinite Dimensions. This work was done while the author was a visitor at the University of Bielefeld. The author would like to thank Prof. W.-J. Beyn for the stimulating discussions. The author is also grateful to the referee for his/her valuable comments.",

year = "2002",

doi = "10.1023/A:1016335115301",

language = "English (US)",

volume = "14",

pages = "549--588",

journal = "Journal of Dynamics and Differential Equations",

issn = "1040-7294",

publisher = "Springer New York",

number = "3",

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TY - JOUR

T1 - Small delay inertial manifolds under numerics

T2 - A numerical structural stability result

AU - Farkas, Gyula

AU - Sell, George R.

N1 - Funding Information: Supported by DAAD project 323-PPP, Qualitative Theory of Numerical Methods for Evolution Equations in Infinite Dimensions. This work was done while the author was a visitor at the University of Bielefeld. The author would like to thank Prof. W.-J. Beyn for the stimulating discussions. The author is also grateful to the referee for his/her valuable comments.

PY - 2002

Y1 - 2002

N2 - In this paper we formulate a numerical structural stability result for delay equations with small delay under Euler discretization. The main ingredients of our approach are the existence and smoothness of small delay inertial manifolds, the C1-closeness of the small delay inertial manifolds and their numerical approximation and M.-C. Li's recent result on numerical structural stability of ordinary differential equations under the Euler method.

AB - In this paper we formulate a numerical structural stability result for delay equations with small delay under Euler discretization. The main ingredients of our approach are the existence and smoothness of small delay inertial manifolds, the C1-closeness of the small delay inertial manifolds and their numerical approximation and M.-C. Li's recent result on numerical structural stability of ordinary differential equations under the Euler method.

KW - C -estimates

KW - Delay equations

KW - Euler method

KW - Numerical structural stability

KW - Small delay inertial manifolds

KW - Smoothness

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U2 - 10.1023/A:1016335115301

DO - 10.1023/A:1016335115301

M3 - Article

AN - SCOPUS:7444219768

SN - 1040-7294

VL - 14

SP - 549

EP - 588

JO - Journal of Dynamics and Differential Equations

JF - Journal of Dynamics and Differential Equations

IS - 3

ER -

Small delay inertial manifolds under numerics: A numerical structural stability result

Abstract

Bibliographical note

Keywords

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