03770nam 22006375 450 99646677050331620200629162635.03-642-34035-010.1007/978-3-642-34035-2(CKB)3400000000102791(SSID)ssj0000855321(PQKBManifestationID)11470365(PQKBTitleCode)TC0000855321(PQKBWorkID)10929226(PQKB)11327155(DE-He213)978-3-642-34035-2(MiAaPQ)EBC3070941(PPN)168325985(EXLCZ)99340000000010279120121215d2013 u| 0engurnn|008mamaatxtccrComposite Asymptotic Expansions[electronic resource] /by Augustin Fruchard, Reinhard Schafke1st ed. 2013.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2013.1 online resource (X, 161 p. 21 illus.) Lecture Notes in Mathematics,0075-8434 ;2066Bibliographic Level Mode of Issuance: Monograph3-642-34034-2 Includes bibliographical references and index.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.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.Lecture Notes in Mathematics,0075-8434 ;2066Approximation theoryDifferential equationsSequences (Mathematics)Approximations and Expansionshttps://scigraph.springernature.com/ontologies/product-market-codes/M12023Ordinary Differential Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12147Sequences, Series, Summabilityhttps://scigraph.springernature.com/ontologies/product-market-codes/M1218XApproximation theory.Differential equations.Sequences (Mathematics).Approximations and Expansions.Ordinary Differential Equations.Sequences, Series, Summability.511.441A6034E34M3034M60mscFruchard Augustinauthttp://id.loc.gov/vocabulary/relators/aut479689Schafke Reinhardauthttp://id.loc.gov/vocabulary/relators/autBOOK996466770503316Composite Asymptotic Expansions2510957UNISA