Word series high-order averaging of highly oscillatory differential equations with delay

We show that, when the delay is an integer multiple of the forcing period, it is possible to obtain easily high-order averaged versions of periodically forced systems of delay differential equations with constant delay. Our approach is based on the use of word series techniques to obtain high-order...

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Main Authors: Sanz-Serna J. M., Zhu Beibei
Format: Article
Language:English
Published: Sciendo 2019-12-01
Series:Applied Mathematics and Nonlinear Sciences
Subjects:
Online Access:https://doi.org/10.2478/AMNS.2019.2.00042
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author Sanz-Serna J. M.
Zhu Beibei
author_facet Sanz-Serna J. M.
Zhu Beibei
author_sort Sanz-Serna J. M.
collection DOAJ
description We show that, when the delay is an integer multiple of the forcing period, it is possible to obtain easily high-order averaged versions of periodically forced systems of delay differential equations with constant delay. Our approach is based on the use of word series techniques to obtain high-order averaged equations for differential equations without delay.
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spelling doaj.art-3ee72ebc41ad40d1abc1604b2a062bf22024-04-02T09:21:10ZengSciendoApplied Mathematics and Nonlinear Sciences2444-86562019-12-014244545410.2478/AMNS.2019.2.00042Word series high-order averaging of highly oscillatory differential equations with delaySanz-Serna J. M.0Zhu Beibei1Departamento de Matemáticas, Universidad Carlos III de Madrid, Avenida de la Universidad 30, E-28911, Leganés (Madrid), SpainNational Center for Mathematics and Interdisciplinary Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, P.R. ChinaWe show that, when the delay is an integer multiple of the forcing period, it is possible to obtain easily high-order averaged versions of periodically forced systems of delay differential equations with constant delay. Our approach is based on the use of word series techniques to obtain high-order averaged equations for differential equations without delay.https://doi.org/10.2478/AMNS.2019.2.00042delay differential equationsstroboscopic averagingword series34c29
spellingShingle Sanz-Serna J. M.
Zhu Beibei
Word series high-order averaging of highly oscillatory differential equations with delay
Applied Mathematics and Nonlinear Sciences
delay differential equations
stroboscopic averaging
word series
34c29
title Word series high-order averaging of highly oscillatory differential equations with delay
title_full Word series high-order averaging of highly oscillatory differential equations with delay
title_fullStr Word series high-order averaging of highly oscillatory differential equations with delay
title_full_unstemmed Word series high-order averaging of highly oscillatory differential equations with delay
title_short Word series high-order averaging of highly oscillatory differential equations with delay
title_sort word series high order averaging of highly oscillatory differential equations with delay
topic delay differential equations
stroboscopic averaging
word series
34c29
url https://doi.org/10.2478/AMNS.2019.2.00042
work_keys_str_mv AT sanzsernajm wordserieshighorderaveragingofhighlyoscillatorydifferentialequationswithdelay
AT zhubeibei wordserieshighorderaveragingofhighlyoscillatorydifferentialequationswithdelay