Composite asymptotic expansions
 Author/Creator
 Fruchard, Augustin.
 Language
 English.
 Imprint
 Heidelberg ; New York : Springer Verlag, c2013.
 Physical description
 x, 161 p. : ill. ; 23 cm.
 Series
 Lecture notes in mathematics (SpringerVerlag) 2066.
Access
Available online
 www.springerlink.com
 dx.doi.org SpringerLink

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QA3 .L28 V.2066

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QA3 .L28 V.2066
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Contributors
 Contributor
 Schäfke, Reinhard.
Contents/Summary
 Bibliography
 Includes bibliographical references and index.
 Contents

 Four introductory examples
 Composite asymptotic expansions : general study
 Composite asymptotic expansions : Gevrey theory
 A theorem of RamisSibuya type
 Composite expansions and singularly perturbed differential equations
 Applications
 Historical remarks.
 Publisher's 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 wellsuited 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 socalled nonsmooth or angular canard solutions. Finally an AckerbergO'Malley resonance problem is solved.
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Subjects
Bibliographic information
 Publication date
 2013
 Responsibility
 Augustin Fruchard, Reinhard Schäfke.
 Series
 Lecture notes in mathematics ; 2066
 Available in another form
 Online version: Fruchard, Augustin. Composite asymptotic expansions. Berlin : Springer, c2013 9783642340352 (OCoLC)822020531
 ISBN
 9783642340345
 3642340342
 9783642340352 (electronic bk.)
 3642340350 (electronic bk.)