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Composite asymptotic expansions

Author: Augustin Fruchard; Reinhard Schäfke
Publisher: Heidelberg ; New York : Springer Verlag, ©2013.
Series: Lecture notes in mathematics (Springer-Verlag), 2066.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
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  Read more...
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Additional Physical Format: Online version:
Fruchard, Augustin.
Composite asymptotic expansions.
Berlin : Springer, ©2013
(OCoLC)822020531
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Augustin Fruchard; Reinhard Schäfke
ISBN: 9783642340345 3642340342
OCLC Number: 812252445
Description: x, 161 pages : illustrations ; 23 cm.
Contents: 1. Four introductory examples --
2. Composite asymptotic expansions : general study --
3. Composite asymptotic expansions : Gevrey theory --
4. A theorem of Ramis-Sibuya type --
5. Composite expansions and singularly perturbed differential equations --
6. Applications --
7. Historical remarks.
Series Title: Lecture notes in mathematics (Springer-Verlag), 2066.
Responsibility: Augustin Fruchard, Reinhard Schäfke.

Abstract:

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  Read more...

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From the reviews:"This memoir develops the theory of Composite Asymptotic Expansions ... . The book is very technical, but written in a clear and precise style. The notions are well motivated, and Read more...

 
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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.<\/span>\"@en<\/a> ;\u00A0\u00A0\u00A0\nschema:description<\/a> \"1. Four introductory examples -- 2. Composite asymptotic expansions : general study -- 3. Composite asymptotic expansions : Gevrey theory -- 4. A theorem of Ramis-Sibuya type -- 5. Composite expansions and singularly perturbed differential equations -- 6. Applications -- 7. 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