Composite Asymptotic Expansions

Name: Composite Asymptotic Expansions
Brand: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
SKU: 9783642340345
Price: 193.22 RON
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Autor: Augustin Fruchard, Reinhard Schäfke

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Editura: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG

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The purpose of these lecture notes is to develop a theory of asymptotic expansions for functions inv...

Informații despre carte

Autor

Augustin Fruchard, Reinhard Schäfke

Limbă

engleză

Legare

Carte - Carte broșată

Publicat

2012

Pagini

161

EAN

9783642340345

ISBN

3642340342

Enbook ID

01662346

Editura

Springer-Verlag Berlin and Heidelberg GmbH & Co. KG

Greutate

286

Dimensiuni

237 x 154 x 14

Descriere completă

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.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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Composite Asymptotic Expansions

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