Composite Asymptotic Expansions

Author : Augustin Fruchard
Publisher : Springer
ISBN 13 : 3642340350
Total Pages : 169 pages
Book Rating : 4.52/5 ( download)

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Download or read book Composite Asymptotic Expansions written by Augustin Fruchard and published by Springer. This book was released on 2012-12-15 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Wolfgang Wasow
Publisher : Courier Dover Publications
ISBN 13 : 0486824586
Total Pages : 385 pages
Book Rating : 4.81/5 ( download)

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Download or read book Asymptotic Expansions for Ordinary Differential Equations written by Wolfgang Wasow and published by Courier Dover Publications. This book was released on 2018-03-21 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: This outstanding text concentrates on the mathematical ideas underlying various asymptotic methods for ordinary differential equations that lead to full, infinite expansions. "A book of great value." — Mathematical Reviews. 1976 revised edition.

Author : Wiktor Eckhaus
Publisher : Elsevier Science & Technology
ISBN 13 :
Total Pages : 168 pages
Book Rating : 4.49/5 ( download)

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Download or read book Matched Asymptotic Expansions and Singular Perturbations written by Wiktor Eckhaus and published by Elsevier Science & Technology. This book was released on 1973 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : P.A. Lagerstrom
Publisher : Springer Science & Business Media
ISBN 13 : 1475719906
Total Pages : 263 pages
Book Rating : 4.01/5 ( download)

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Download or read book Matched Asymptotic Expansions written by P.A. Lagerstrom and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: Content and Aims of this Book Earlier drafts of the manuscript of this book (James A. Boa was then coau thor) contained discussions of many methods and examples of singular perturba tion problems. The ambitious plans of covering a large number of topics were later abandoned in favor of the present goal: a thorough discussion of selected ideas and techniques used in the method of matched asymptotic expansions. Thus many problems and methods are not covered here: the method of av eraging and the related method of multiple scales are mentioned mainly to give reasons why they are not discussed further. Examples which required too sophis ticated and involved calculations, or advanced knowledge of a special field, are not treated; for instance, to the author's regret some very interesting applications to fluid mechanics had to be omitted for this reason. Artificial mathematical examples introduced to show some exotic or unexpected behavior are omitted, except when they are analytically simple and are needed to illustrate mathematical phenomena important for realistic problems. Problems of numerical analysis are not discussed.

Author :
Publisher :
ISBN 13 :
Total Pages : 24 pages
Book Rating : 4.81/5 ( download)

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Download or read book Solution of Second-order Linear System by Matched Asymptotic Expansions written by and published by . This book was released on 1982 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Vladimir A. Smirnov
Publisher : Springer
ISBN 13 : 3540445749
Total Pages : 270 pages
Book Rating : 4.46/5 ( download)

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Download or read book Applied Asymptotic Expansions in Momenta and Masses written by Vladimir A. Smirnov and published by Springer. This book was released on 2003-07-01 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'The sturgeon they sent was second grade fresh,' said the barman. 'Really, what nonsense/' 'Why nonsense?' '"Second grade fresh" that's what I call nonsense/ There's only one degree of freshness the first, and it's the last) (M. A. Bulgakov, The Master and Margarita) The goal of this book is to describe in detail how Feynman integrals can be expanded in suitable parameters, when various momenta or masses are small or large. In a narrow sense, this problem is connected with practical calcula tions. In a situation where a given Feynman integral depends on parameters of very different scales, a natural idea is to replace it by a sufficiently large number of terms of an expansion of it in ratios of small and large scales. It will be explained how this problem of expansion can be systematically solved, by formulating universal prescriptions that express terms of the expansion by using the original Feynman integral with its integrand expanded into a Taylor series in appropriate momenta and masses. It turns out that knowledge of the structure of the asymptotic expansion at the diagrammatic level is a key point in understanding how to perform expansions at the operator level. There are various examples of these ex pansions: the operator product expansion, the large mass expansion, Heavy Quark Effective Theory, Non Relativistic QCD, etc. Each of them serves as a realization of the factorization of contributions of different scales.

Author : A. Georgescu
Publisher : CRC Press
ISBN 13 : 9780412558603
Total Pages : 282 pages
Book Rating : 4.02/5 ( download)

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Download or read book Asymptotic Treatment of Differential Equations written by A. Georgescu and published by CRC Press. This book was released on 1995-05-15 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main definitions and results of asymptotic analysis and the theory of regular and singular perturbations are summarized in this book. They are applied to the asymptotic study of several mathematical models from mechanics, fluid dynamics, statistical mechanics, meteorology and elasticity. Due to the generality of presentation this applications-oriented book is suitable for the solving of differential equations from any other field of interest.

Author : Robert B. Dingle
Publisher :
ISBN 13 :
Total Pages : 556 pages
Book Rating : 4.74/5 ( download)

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Download or read book Asymptotic Expansions: Their Derivation and Interpretation written by Robert B. Dingle and published by . This book was released on 1973 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : E. T. Copson
Publisher : Cambridge University Press
ISBN 13 : 9780521604826
Total Pages : 136 pages
Book Rating : 4.26/5 ( download)

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Download or read book Asymptotic Expansions written by E. T. Copson and published by Cambridge University Press. This book was released on 2004-06-03 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: Asymptotic representation of a function os of great importance in many branches of pure and applied mathematics.

Author : Wolfgang Richard Wasow
Publisher :
ISBN 13 :
Total Pages : 362 pages
Book Rating : 4.19/5 ( download)

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Download or read book Asymptotic Expansions for Ordinary Differential Equations written by Wolfgang Richard Wasow and published by . This book was released on 1965 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: