Lecture Notes in Mathematics

Composite Asymptotic Expansions

Authors: Fruchard, Augustin, Schafke, Reinhard

  • Presents a comprehensive theory of infinite composite asymptotic expansions (CAsEs), an alternative to the method of matched asymptotic expansions
  • Generalizes the classical theory of Gevrey asymptotic expansions to such CAsEs, thus establishing a new powerful tool for the study of turning points of singularly perturbed ODEs
  • Using CAsEs, especially their versions of Gevrey type, to obtain new results for three classical problems in the theory of singularly perturbed ODEs
see more benefits

Buy this book

eBook $34.99
price for USA (gross)
  • ISBN 978-3-642-34035-2
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.95
price for USA
  • ISBN 978-3-642-34034-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
About this book

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.

Reviews

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 many examples are given. … this book will be of great interest to people studying asymptotics for singularly perturbed differential equations.” (Jorge Mozo Fernández, Mathematical Reviews, December, 2013)

“This book focuses on the theory of composite asymptotic expansions for functions of two variables when functions of one variable and functions of the quotient of these two variables are used at the same time. … The book addresses graduate students and researchers in asymptotic analysis and applications.” (Vladimir Sobolev, zbMATH, Vol. 1269, 2013)

Table of contents (7 chapters)

  • Four Introductory Examples

    Fruchard, Augustin (et al.)

    Pages 1-15

  • Composite Asymptotic Expansions: General Study

    Fruchard, Augustin (et al.)

    Pages 17-41

  • Composite Asymptotic Expansions: Gevrey Theory

    Fruchard, Augustin (et al.)

    Pages 43-61

  • A Theorem of Ramis–Sibuya Type

    Fruchard, Augustin (et al.)

    Pages 63-80

  • Composite Expansions and Singularly Perturbed Differential Equations

    Fruchard, Augustin (et al.)

    Pages 81-118

Buy this book

eBook $34.99
price for USA (gross)
  • ISBN 978-3-642-34035-2
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.95
price for USA
  • ISBN 978-3-642-34034-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Composite Asymptotic Expansions
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
2066
Copyright
2013
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-34035-2
DOI
10.1007/978-3-642-34035-2
Softcover ISBN
978-3-642-34034-5
Series ISSN
0075-8434
Edition Number
1
Number of Pages
X, 161
Number of Illustrations and Tables
21 b/w illustrations
Topics