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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Format: | Article |
Language: | English |
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Sciendo
2019-12-01
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Series: | Applied Mathematics and Nonlinear Sciences |
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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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format | Article |
id | doaj.art-3ee72ebc41ad40d1abc1604b2a062bf2 |
institution | Directory Open Access Journal |
issn | 2444-8656 |
language | English |
last_indexed | 2024-04-24T15:15:50Z |
publishDate | 2019-12-01 |
publisher | Sciendo |
record_format | Article |
series | Applied Mathematics and Nonlinear Sciences |
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 |