Composite asymptotic expansions Augustin Fruchard, Reinhard Schäfke

Format:

Book

Author/Creator:

Fruchard, Augustin

Contributor:

Schäfke, Reinhard

Series:

Lecture notes in mathematics (Springer-Verlag) 2066

Lecture notes in mathematics 1617-9692 2066

Language:

English

Subjects (All):

Asymptotic expansions.

Differential equations--Asymptotic theory.

Differential equations.

Integral equations--Asymptotic theory.

Integral equations.

Physical Description:

1 online resource

Place of Publication:

Berlin Springer ©2013

Language Note:

English

System Details:

text file

PDF

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

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

Notes:

Includes bibliographical references and index

Online resource; title from PDF title page (SpringerLink, viewed December 19, 2012)

Other Format:

Printed edition:

ISBN:

9783642340352

3642340350

OCLC:

822020531

Access Restriction:

Restricted for use by site license