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020 _a9783642340352
_9978-3-642-34035-2
024 7 _a10.1007/978-3-642-34035-2
_2doi
050 4 _aQA401-425
072 7 _aPBKJ
_2bicssc
072 7 _aMAT034000
_2bisacsh
072 7 _aPBKJ
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082 0 4 _a511.4
_223
100 1 _aFruchard, Augustin.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aComposite Asymptotic Expansions
_h[electronic resource] /
_cby Augustin Fruchard, Reinhard Schäfke.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2013.
300 _aX, 161 p. 21 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2066
505 0 _aFour 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 _aThe 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 _aMathematics.
650 0 _aDifferential Equations.
650 0 _aSequences (Mathematics).
650 1 4 _aApproximations and Expansions.
_0http://scigraph.springernature.com/things/product-market-codes/M12023
650 2 4 _aOrdinary Differential Equations.
_0http://scigraph.springernature.com/things/product-market-codes/M12147
650 2 4 _aSequences, Series, Summability.
_0http://scigraph.springernature.com/things/product-market-codes/M1218X
700 1 _aSchäfke, Reinhard.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642340369
776 0 8 _iPrinted edition:
_z9783642340345
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2066
856 4 0 _uhttps://doi.org/10.1007/978-3-642-34035-2
912 _aZDB-2-SMA
912 _aZDB-2-LNM
999 _c11644
_d11644