Composite Asymptotic Expansions

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...

Descripción completa

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Fruchard, Augustin (Autor), Schafke, Reinhard (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2013.
Edición:1st ed. 2013.
Colección:Lecture Notes in Mathematics, 2066
Temas:
Approximation theory.
Differential equations.
Sequences (Mathematics).
Approximations and Expansions.
Differential Equations.
Sequences, Series, Summability.
Acceso en línea:Texto Completo

MARC

LEADER 00000nam a22000005i 4500
001 978-3-642-34035-2
003 DE-He213
005 20220112114933.0
007 cr nn 008mamaa
008 121215s2013 gw | s |||| 0|eng d
020 |a 9783642340352  |9 978-3-642-34035-2 
024 7 |a 10.1007/978-3-642-34035-2  |2 doi 
050 4 |a QA221-224 
072 7 |a PBKJ  |2 bicssc 
072 7 |a MAT034000  |2 bisacsh 
072 7 |a PBKJ  |2 thema 
082 0 4 |a 511.4  |2 23 
100 1 |a Fruchard, Augustin.  |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
245 1 0 |a Composite Asymptotic Expansions  |h [electronic resource] /  |c by Augustin Fruchard, Reinhard Schafke. 
250 |a 1st ed. 2013. 
264 1 |a Berlin, Heidelberg :  |b Springer Berlin Heidelberg :  |b Imprint: Springer,  |c 2013. 
300 |a X, 161 p. 21 illus.  |b online resource. 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
347 |a text file  |b PDF  |2 rda 
490 1 |a Lecture Notes in Mathematics,  |x 1617-9692 ;  |v 2066 
505 0 |a 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. 
520 |a 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. 
650 0 |a Approximation theory. 
650 0 |a Differential equations. 
650 0 |a Sequences (Mathematics). 
650 1 4 |a Approximations and Expansions. 
650 2 4 |a Differential Equations. 
650 2 4 |a Sequences, Series, Summability. 
700 1 |a Schafke, Reinhard.  |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
710 2 |a SpringerLink (Online service) 
773 0 |t Springer Nature eBook 
776 0 8 |i Printed edition:  |z 9783642340369 
776 0 8 |i Printed edition:  |z 9783642340345 
830 0 |a Lecture Notes in Mathematics,  |x 1617-9692 ;  |v 2066 
856 4 0 |u https://doi.uam.elogim.com/10.1007/978-3-642-34035-2  |z Texto Completo 
912 |a ZDB-2-SMA 
912 |a ZDB-2-SXMS 
912 |a ZDB-2-LNM 
950 |a Mathematics and Statistics (SpringerNature-11649) 
950 |a Mathematics and Statistics (R0) (SpringerNature-43713) 

Ejemplares similares