The Asymptotic Solution Of Linear Differential Systems
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Asymptotic Analysis
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Author : Mikhail V. Fedoryuk
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Asymptotic Analysis written by Mikhail V. Fedoryuk and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
The Asymptotic Solution Of Linear Differential Systems
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Author : Michael Stephen Patrick Eastham
language : en
Publisher: Oxford University Press, USA
Release Date : 1989
The Asymptotic Solution Of Linear Differential Systems written by Michael Stephen Patrick Eastham and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Language Arts & Disciplines categories.
An account from 1975-1988 of the developments in the application of the modern asymptotic theory of linear differential systems, which dates from the Levinson Theorem of 1948. The main results and techniques are identified and earlier results are placed in a wider context.
Asymptotic Expansions For Ordinary Differential Equations
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Author : Wolfgang Wasow
language : en
Publisher: Courier Dover Publications
Release Date : 2018-03-21
Asymptotic Expansions For Ordinary Differential Equations written by Wolfgang Wasow and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-21 with Mathematics categories.
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.
Asymptotic Properties Of Solutions Of Nonautonomous Ordinary Differential Equations
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Author : Ivan Kiguradze
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Asymptotic Properties Of Solutions Of Nonautonomous Ordinary Differential Equations written by Ivan Kiguradze and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
The Asymptotic Solution Of Linear Differential Equations Of The Second Order In A Domain Containing One Transition Point
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Author : Frank W. J. Olver
language : en
Publisher:
Release Date : 1956
The Asymptotic Solution Of Linear Differential Equations Of The Second Order In A Domain Containing One Transition Point written by Frank W. J. Olver and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1956 with categories.
Asymptotic Solutions Of Differential Equations And Their Applications
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Author : Calvin Hayden Wilcox
language : en
Publisher:
Release Date : 1964
Asymptotic Solutions Of Differential Equations And Their Applications written by Calvin Hayden Wilcox and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1964 with Mathematics categories.
Asymptotic Integration Of Differential And Difference Equations
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Author : Sigrun Bodine
language : en
Publisher: Springer
Release Date : 2015-05-26
Asymptotic Integration Of Differential And Difference Equations written by Sigrun Bodine and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-26 with Mathematics categories.
This book presents the theory of asymptotic integration for both linear differential and difference equations. This type of asymptotic analysis is based on some fundamental principles by Norman Levinson. While he applied them to a special class of differential equations, subsequent work has shown that the same principles lead to asymptotic results for much wider classes of differential and also difference equations. After discussing asymptotic integration in a unified approach, this book studies how the application of these methods provides several new insights and frequent improvements to results found in earlier literature. It then continues with a brief introduction to the relatively new field of asymptotic integration for dynamic equations on time scales. Asymptotic Integration of Differential and Difference Equations is a self-contained and clearly structured presentation of some of the most important results in asymptotic integration and the techniques used in this field. It will appeal to researchers in asymptotic integration as well to non-experts who are interested in the asymptotic analysis of linear differential and difference equations. It will additionally be of interest to students in mathematics, applied sciences, and engineering. Linear algebra and some basic concepts from advanced calculus are prerequisites.
Asymptotics Of Linear Differential Equations
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Author : M.H. Lantsman
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Asymptotics Of Linear Differential Equations written by M.H. Lantsman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
The asymptotic theory deals with the problern of determining the behaviour of a function in a neighborhood of its singular point. The function is replaced by another known function ( named the asymptotic function) close (in a sense) to the function under consideration. Many problems of mathematics, physics, and other divisions of natural sci ence bring out the necessity of solving such problems. At the present time asymptotic theory has become an important and independent branch of mathematical analysis. The present consideration is mainly based on the theory of asymp totic spaces. Each asymptotic space is a collection of asymptotics united by an associated real function which determines their growth near the given point and (perhaps) some other analytic properties. The main contents of this book is the asymptotic theory of ordinary linear differential equations with variable coefficients. The equations with power order growth coefficients are considered in detail. As the application of the theory of differential asymptotic fields, we also consider the following asymptotic problems: the behaviour of explicit and implicit functions, improper integrals, integrals dependent on a large parameter, linear differential and difference equations, etc .. The obtained results have an independent meaning. The reader is assumed to be familiar with a comprehensive course of the mathematical analysis studied, for instance at mathematical departments of universities. Further necessary information is given in this book in summarized form with proofs of the main aspects.
The Asymptotic Solution Of Linear Differential Equations Of The Second Order For Large Values Of A Parameter
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Author : Frank W. J. Olver
language : en
Publisher:
Release Date : 1954
The Asymptotic Solution Of Linear Differential Equations Of The Second Order For Large Values Of A Parameter written by Frank W. J. Olver and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1954 with categories.
On The Asymptotic Solution Of The Non Homogeneous Linear Differential Equation Of The N Th Order A Particular Solution
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Author : WILLIAM VAN NEST GARRETSON
language : en
Publisher:
Release Date : 1916
On The Asymptotic Solution Of The Non Homogeneous Linear Differential Equation Of The N Th Order A Particular Solution written by WILLIAM VAN NEST GARRETSON and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1916 with categories.