Composite asymptotic expansions /

Composite asymptotic expansions /

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Bibliographic Details
Author / Creator:	Fruchard, Augustin.
Imprint:	Berlin : Springer, ©2013.
Description:	1 online resource (x, 161 pages) : illustrations.
Language:	English
Series:	Lecture notes in mathematics, 1617-9692 ; 2066 Lecture notes in mathematics (Springer-Verlag) ; 2066.
Subject:	Asymptotic expansions. Differential equations -- Asymptotic theory. Integral equations -- Asymptotic theory. Asymptotic expansions. Differential equations -- Asymptotic theory. Integral equations -- Asymptotic theory.
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/11077756

Hidden Bibliographic Details
Other authors / contributors:	Schäfke, Reinhard.
ISBN:	9783642340352 3642340350 9783642340345 3642340342
Notes:	Includes bibliographical references and index. Online resource; title from PDF title page (SpringerLink, viewed Dec. 19, 2012).
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 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.

Table of Contents:

Four Introductory Examples
Composite Asymptotic Expansions: General Study
Composite Asymptotic Expansions: Gevrey Theory
A Theorem of Ramis-Sibuya Type
Composite Expansions and Singularly Perturbed Differential Equations
Applications
Historical Remarks.