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Composite asymptotic expansions

The purpose of these lecture notes is to develop a theory of asymptotic expansions for functions involving two variables, while at the same time using functions involving one variable and functions of the quotient of these two variables. Such composite asymptotic expansions (CAsEs) are particularly...

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Detalles Bibliográficos
Autores principales: Fruchard, Augustin, Schäfke, Reinhard
Lenguaje:eng
Publicado: Springer 2013
Materias:
Acceso en línea:https://dx.doi.org/10.1007/978-3-642-34035-2
http://cds.cern.ch/record/1691815
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author Fruchard, Augustin
Schäfke, Reinhard
author_facet Fruchard, Augustin
Schäfke, Reinhard
author_sort Fruchard, Augustin
collection CERN
description The purpose of these lecture notes is to develop a theory of asymptotic expansions for functions involving two variables, while at the same time using functions involving one variable and functions of the quotient of these two variables. Such composite asymptotic expansions (CAsEs) are particularly well-suited to describing solutions of singularly perturbed ordinary differential equations near turning points. CAsEs imply inner and outer expansions near turning points. Thus our approach is closely related to the method of matched asymptotic expansions. CAsEs offer two unique advantages, however. First, they provide uniform expansions near a turning point and away from it. Second, a Gevrey version of CAsEs is available and detailed in the lecture notes. Three problems are presented in which CAsEs are useful. The first application concerns canard solutions near a multiple turning point. The second application concerns so-called non-smooth or angular canard solutions. Finally an Ackerberg-O’Malley resonance problem is solved.
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spelling cern-16918152021-04-21T21:06:50Zdoi:10.1007/978-3-642-34035-2http://cds.cern.ch/record/1691815engFruchard, AugustinSchäfke, ReinhardComposite asymptotic expansionsMathematical Physics and MathematicsThe purpose of these lecture notes is to develop a theory of asymptotic expansions for functions involving two variables, while at the same time using functions involving one variable and functions of the quotient of these two variables. Such composite asymptotic expansions (CAsEs) are particularly well-suited to describing solutions of singularly perturbed ordinary differential equations near turning points. CAsEs imply inner and outer expansions near turning points. Thus our approach is closely related to the method of matched asymptotic expansions. CAsEs offer two unique advantages, however. First, they provide uniform expansions near a turning point and away from it. Second, a Gevrey version of CAsEs is available and detailed in the lecture notes. Three problems are presented in which CAsEs are useful. The first application concerns canard solutions near a multiple turning point. The second application concerns so-called non-smooth or angular canard solutions. Finally an Ackerberg-O’Malley resonance problem is solved.Springeroai:cds.cern.ch:16918152013
spellingShingle Mathematical Physics and Mathematics
Fruchard, Augustin
Schäfke, Reinhard
Composite asymptotic expansions
title Composite asymptotic expansions
title_full Composite asymptotic expansions
title_fullStr Composite asymptotic expansions
title_full_unstemmed Composite asymptotic expansions
title_short Composite asymptotic expansions
title_sort composite asymptotic expansions
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1007/978-3-642-34035-2
http://cds.cern.ch/record/1691815
work_keys_str_mv AT fruchardaugustin compositeasymptoticexpansions
AT schafkereinhard compositeasymptoticexpansions