The Resource Composite Asymptotic Expansions, by Augustin Fruchard, Reinhard Schäfke, (electronic resource)

Composite Asymptotic Expansions, by Augustin Fruchard, Reinhard Schäfke, (electronic resource)

Label
Composite Asymptotic Expansions
Title
Composite Asymptotic Expansions
Statement of responsibility
by Augustin Fruchard, Reinhard Schäfke
Creator
Contributor
Author
Provider
Subject
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
http://library.link/vocab/creatorName
Fruchard, Augustin
Image bit depth
0
LC call number
QA401-425
Literary form
non fiction
http://library.link/vocab/relatedWorkOrContributorName
  • Schäfke, Reinhard.
  • SpringerLink
Series statement
Lecture Notes in Mathematics,
Series volume
2066
http://library.link/vocab/subjectName
  • Mathematics
  • Differential Equations
  • Sequences (Mathematics)
  • Mathematics
  • Approximations and Expansions
  • Ordinary Differential Equations
  • Sequences, Series, Summability
Label
Composite Asymptotic Expansions, by Augustin Fruchard, Reinhard Schäfke, (electronic resource)
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
txt
Content type MARC source
rdacontent
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
X, 161 p. 21 illus.
File format
multiple file formats
Form of item
electronic
Isbn
9783642340352
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1007/978-3-642-34035-2
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-642-34035-2
Label
Composite Asymptotic Expansions, by Augustin Fruchard, Reinhard Schäfke, (electronic resource)
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
txt
Content type MARC source
rdacontent
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
X, 161 p. 21 illus.
File format
multiple file formats
Form of item
electronic
Isbn
9783642340352
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1007/978-3-642-34035-2
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(DE-He213)978-3-642-34035-2

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