The Resource Composite asymptotic expansions, Augustin Fruchard, Reinhard Schäfke, (electronic resource)

Composite asymptotic expansions, Augustin Fruchard, Reinhard Schäfke, (electronic resource)

Label
Composite asymptotic expansions
Title
Composite asymptotic expansions
Statement of responsibility
Augustin Fruchard, Reinhard Schäfke
Creator
Contributor
Subject
Genre
Language
eng
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
Member of
Cataloging source
HNK
http://library.link/vocab/creatorName
Fruchard, Augustin
Dewey number
511/.4
Illustrations
illustrations
Index
index present
LC call number
QA431
LC item number
.F78 2013eb
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorName
  • Schäfke, Reinhard
  • SpringerLink (Online service)
Series statement
Lecture notes in mathematics,
Series volume
2066
http://library.link/vocab/subjectName
  • Asymptotic expansions
  • Differential equations
  • Integral equations
Label
Composite asymptotic expansions, Augustin Fruchard, Reinhard Schäfke, (electronic resource)
Link
http://libraries.ou.edu/access.aspx?url=http://dx.doi.org/10.1007/978-3-642-34035-2
Instantiates
Publication
Bibliography note
Includes bibliographical references and index
Color
multicolored
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 -- References -- Index
Dimensions
unknown
Extent
1 online resource (x, 161 p.)
Form of item
online
Isbn
9783642340352
Isbn Type
(electronic bk.)
Other physical details
ill.
Sound
unknown sound
Specific material designation
remote
System control number
  • 4089859-01okla_normanlaw
  • (SIRSI)4089859
  • (Sirsi) o822020531
  • (OCoLC)822020531
Label
Composite asymptotic expansions, Augustin Fruchard, Reinhard Schäfke, (electronic resource)
Link
http://libraries.ou.edu/access.aspx?url=http://dx.doi.org/10.1007/978-3-642-34035-2
Publication
Bibliography note
Includes bibliographical references and index
Color
multicolored
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 -- References -- Index
Dimensions
unknown
Extent
1 online resource (x, 161 p.)
Form of item
online
Isbn
9783642340352
Isbn Type
(electronic bk.)
Other physical details
ill.
Sound
unknown sound
Specific material designation
remote
System control number
  • 4089859-01okla_normanlaw
  • (SIRSI)4089859
  • (Sirsi) o822020531
  • (OCoLC)822020531

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