Asymptotic Expansions The Asymptotic Behaviour Of The Real Solutions Of Certain Second Order Differential Equations

Author : Johannes Gualtherus van der Corput
Publisher :
ISBN 13 :
Total Pages : 356 pages
Book Rating : 4.20/5 ( download)

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Download or read book Asymptotic Expansions: The asymptotic behaviour of the real solutions of certain second order differential equations written by Johannes Gualtherus van der Corput and published by . This book was released on 1955 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : J. Grander Corput
Publisher :
ISBN 13 :
Total Pages : 171 pages
Book Rating : 4.26/5 ( download)

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Download or read book The Asymptotic Behaviour of the Real Solutions of Certain Second Order Differential Equations written by J. Grander Corput and published by . This book was released on 1955 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Johannes Gualtherus van der Corput
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.22/5 ( download)

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Download or read book Asymptotic Expansions written by Johannes Gualtherus van der Corput and published by . This book was released on 1954 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

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 : 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 : A. H. Lightstone
Publisher : Elsevier
ISBN 13 : 1483257444
Total Pages : 215 pages
Book Rating : 4.40/5 ( download)

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Download or read book Nonarchimedean Fields and Asymptotic Expansions written by A. H. Lightstone and published by Elsevier. This book was released on 2016-06-03 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: North-Holland Mathematical Library, Volume 13: Nonarchimedean Fields and Asymptotic Expansions focuses on the connection between nonarchimedean systems and the orders of infinity and smallness that are related with the asymptotic behavior of a function. The publication first explains nonarchimedean fields and nonstandard analysis. Discussions focus on the method of mathematical logic, ultrapower construction, principles of permanence, internal functions, many-sorted structures, nonarchimedean fields and groups, and fields with evaluation. The text then discusses the Euler-Maclaurin expansions and the formal concept of asymptotic expansions. Topics include a generalized criterion for asymptotic expansions, asymptotic power series, Watson's Lemma, asymptotic sequences, and the Euler-Maclaurin formula. The manuscript examines Popken space, including asymptotically finite functions, convergence, norm, algebraic properties of the norm, and Popken's description of the norm. The text is a dependable reference for mathematicians and researchers interested in nonarchimedean fields and asymptotic expansions.

Author : Mikhail V. Fedoryuk
Publisher : Springer Science & Business Media
ISBN 13 : 3642580165
Total Pages : 370 pages
Book Rating : 4.61/5 ( download)

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Download or read book Asymptotic Analysis written by Mikhail V. Fedoryuk and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book we present the main results on the asymptotic theory of ordinary linear differential equations and systems where there is a small parameter in the higher derivatives. We are concerned with the behaviour of solutions with respect to the parameter and for large values of the independent variable. The literature on this question is considerable and widely dispersed, but the methods of proofs are sufficiently similar for this material to be put together as a reference book. We have restricted ourselves to homogeneous equations. The asymptotic behaviour of an inhomogeneous equation can be obtained from the asymptotic behaviour of the corresponding fundamental system of solutions by applying methods for deriving asymptotic bounds on the relevant integrals. We systematically use the concept of an asymptotic expansion, details of which can if necessary be found in [Wasow 2, Olver 6]. By the "formal asymptotic solution" (F.A.S.) is understood a function which satisfies the equation to some degree of accuracy. Although this concept is not precisely defined, its meaning is always clear from the context. We also note that the term "Stokes line" used in the book is equivalent to the term "anti-Stokes line" employed in the physics literature.

Author : Arthur Erdélyi
Publisher :
ISBN 13 :
Total Pages : 22 pages
Book Rating : 4.29/5 ( download)

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Download or read book Asymptotic Solutions of Differential Equations with Transition Points written by Arthur Erdélyi and published by . This book was released on 1956 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Ivan Kiguradze
Publisher : Springer Science & Business Media
ISBN 13 : 9401118086
Total Pages : 343 pages
Book Rating : 4.88/5 ( download)

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Download or read book Asymptotic Properties of Solutions of Nonautonomous Ordinary Differential Equations written by Ivan Kiguradze and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides a comprehensive review of the developments which have taken place during the last thirty years concerning the asymptotic properties of solutions of nonautonomous ordinary differential equations. The conditions of oscillation of solutions are established, and some general theorems on the classification of equations according to their oscillatory properties are proved. In addition, the conditions are found under which nonlinear equations do not have singular, proper, oscillatory and monotone solutions. The book has five chapters: Chapter I deals with linear differential equations; Chapter II with quasilinear equations; Chapter III with general nonlinear differential equations; and Chapter IV and V deal, respectively, with higher-order and second-order differential equations of the Emden-Fowler type. Each section contains problems, including some which presently remain unsolved. The volume concludes with an extensive list of references. For researchers and graduate students interested in the qualitative theory of differential equations.

Author : R. B. Paris
Publisher : Longman
ISBN 13 :
Total Pages : 364 pages
Book Rating : 4.51/5 ( download)

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Download or read book Asymptotics of High Order Differential Equations written by R. B. Paris and published by Longman. This book was released on 1986 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: