Asymptotic Treatment Of Differential Equations

Author : A. Georgescu
Publisher : CRC Press
Page : 282 pages
File Size : 43,9 Mb
Release : 1995-05-15
Category : Mathematics
ISBN : 0412558602

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Asymptotic Treatment of Differential Equations by A. Georgescu Pdf

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 : R. B. White
Publisher : World Scientific
Page : 430 pages
File Size : 40,6 Mb
Release : 2010
Category : Mathematics
ISBN : 9781848166073

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Asymptotic Analysis of Differential Equations by R. B. White Pdf

"This is a useful volume in which a wide selection of asymptotic techniques is clearly presented in a form suitable for both applied mathematicians and Physicists who require an introduction to asymptotic techniques." --Book Jacket.

Author : Douglas S Jones
Publisher : World Scientific
Page : 176 pages
File Size : 43,6 Mb
Release : 1997-01-16
Category : Electronic
ISBN : 9789814497961

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Introduction To Asymptotics - A Treatment Using Nonstandard Analysis by Douglas S Jones Pdf

Many branches of science and engineering involve applications of mathematical analysis. An important part of applied analysis is asymptotic approximation which is, therefore, an active area of research with new methods and publications being found constantly. This book gives an introduction to the subject sufficient for scientists and engineers to grasp the fundamental techniques, both those which have been known for some time and those which have been discovered more recently. The asymptotic approximation of both integrals and differential equations is discussed and the discussion includes hyperasymptotics as well as uniform asymptotics. There are many numerical examples to illustrate the relation between theory and practice. Exercises in the chapters enable the book to be used as a text for an introductory course.

Author : Ivan Kiguradze,T.A. Chanturia
Publisher : Springer Science & Business Media
Page : 343 pages
File Size : 46,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401118088

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Asymptotic Properties of Solutions of Nonautonomous Ordinary Differential Equations by Ivan Kiguradze,T.A. Chanturia Pdf

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 : Sigrun Bodine,Donald A. Lutz
Publisher : Springer
Page : 402 pages
File Size : 42,5 Mb
Release : 2015-05-26
Category : Mathematics
ISBN : 9783319182483

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Asymptotic Integration of Differential and Difference Equations by Sigrun Bodine,Donald A. Lutz Pdf

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.

Author : Drumi D Bainov,Pavel Simeonov
Publisher : World Scientific
Page : 246 pages
File Size : 49,9 Mb
Release : 1995-03-29
Category : Mathematics
ISBN : 9789814501880

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Impulsive Differential Equations: Asymptotic Properties Of The Solutions by Drumi D Bainov,Pavel Simeonov Pdf

The question of the presence of various asymptotic properties of the solutions of ordinary differential equations arises when solving various practical problems. The investigation of these questions is still more important for impulsive differential equations which have a wider field of application than the ordinary ones.The results obtained by treating the asymptotic properties of the solutions of impulsive differential equations can be found in numerous separate articles. The systematized exposition of these results in a separate book will satisfy the growing interest in the problems related to the asymptotic properties of the solutions of impulsive differential equations and their applications.

Author : Michel Marie Chipot
Publisher : World Scientific
Page : 264 pages
File Size : 48,6 Mb
Release : 2016-06-14
Category : Mathematics
ISBN : 9781783268931

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Asymptotic Issues for Some Partial Differential Equations by Michel Marie Chipot Pdf

Much progress has been made in recent years on the issue of asymptotic behavior of problems set in cylinders. This book goes one step further by presenting the latest accomplishments on asymptotic behavior in domains which become unbounded. It also investigates new issues which have emerged including existence and uniqueness of solution in unbounded domains, anisotropic singular perturbations, periodic behavior forced by periodic data. These new advances are treated with original techniques developed to investigate the asymptotic behavior of various problems. Theories investigated throughout the book can be applied to other problems related to partial differential equations, making it an important text for students and researchers within the discipline. Asymptotic Issues for Some Partial Differential Equations is an updated account of ℓ Goes to Plus Infinity, published by Birkhäuser in 2002. Contents:IntroductionThe Dirichlet Problem in Some Unbounded DomainsThe Pure Neumann ProblemPeriodic ProblemsAnisotropic Singular Perturbation ProblemsEigenvalue ProblemsElliptic SystemsThe Stokes ProblemVariational InequalitiesCalculus of Variations Readership: The book can be used as an academic resource for graduate students and researchers in applied mathematics and engineering.

Author : Douglas Samuel Jones
Publisher : World Scientific
Page : 184 pages
File Size : 52,7 Mb
Release : 1997
Category : Mathematics
ISBN : 9810229151

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Introduction to Asymptotics by Douglas Samuel Jones Pdf

"A very attractive feature of the book is the numerous examples illustrating the methods. A fine collection of exercises enriches each chapter, challenging the reader to check his progress in understanding the methods".Mathematical Reviews"As an introductory book to asymptotics, with chapters on uniform asymptotics and exponential asymptotics, this book clearly fills a gap it has a friendly size and contains many convincing numerical examples and interesting exercises. Hence, I recommend the book to everyone who works in asymptotics".SIAM, 1998" it is an excellent book that contains interesting results and methods for the researchers. It will be useful for the students interested in analysis and lectures on asymptotic methods The reviewer recommends the book to everyone who is interested in analysis, engineers and specialists in ODE-s"Acta Sci. Math. (Szeged), 1999

Author : Wolfgang Wasow
Publisher : Courier Dover Publications
Page : 385 pages
File Size : 51,9 Mb
Release : 2018-03-21
Category : Mathematics
ISBN : 9780486824581

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Asymptotic Expansions for Ordinary Differential Equations by Wolfgang Wasow Pdf

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 : Richard Bellman,Kenneth L. Cooke
Publisher : American Mathematical Soc.
Page : 99 pages
File Size : 47,6 Mb
Release : 1959
Category : Difference equations
ISBN : 9780821812358

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Asymptotic Behavior of Solutions of Differential-Difference Equations by Richard Bellman,Kenneth L. Cooke Pdf

Author : Stepan Fedorovich Feshchenko,Nikolaĭ Ivanovich Shkilʹ,Larisa Danilovna Nikolenko
Publisher : Unknown
Page : 298 pages
File Size : 47,9 Mb
Release : 1967
Category : Asymptotic expansions
ISBN : UOM:39015001316994

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Asymptotic Methods in the Theory of Linear Differential Equations by Stepan Fedorovich Feshchenko,Nikolaĭ Ivanovich Shkilʹ,Larisa Danilovna Nikolenko Pdf

Author : Mikhail V. Fedoryuk
Publisher : Springer Science & Business Media
Page : 370 pages
File Size : 53,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642580161

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Asymptotic Analysis by Mikhail V. Fedoryuk Pdf

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 : Ashwani K. Kapila
Publisher : Unknown
Page : 134 pages
File Size : 40,6 Mb
Release : 1983
Category : Science
ISBN : UOM:39015016003710

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Asymptotic Treatment of Chemically Reacting Systems by Ashwani K. Kapila Pdf

Author : Michel Marie Chipot
Publisher : World Scientific
Page : 283 pages
File Size : 54,5 Mb
Release : 2024-04-15
Category : Mathematics
ISBN : 9789811290459

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Asymptotic Issues For Some Partial Differential Equations (Second Edition) by Michel Marie Chipot Pdf

The primary focus of the book is to explore the asymptotic behavior of problems formulated within cylindrical structures. Various physical applications are discussed, with certain topics such as fluid flows in channels being particularly noteworthy. Additionally, the book delves into the relevance of elasticity in the context of cylindrical bodies.In specific scenarios where the size of the cylinder becomes exceptionally large, the material's behavior is determined solely by its cross-section. The investigation centers around understanding these particular properties.Since the publication of the first edition, several significant advancements have been made, adding depth and interest to the content. Consequently, new sections have been incorporated into the existing edition, complemented by a comprehensive list of references.

Author : R.P. Kuzmina
Publisher : Springer Science & Business Media
Page : 375 pages
File Size : 46,6 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9789401593472

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Asymptotic Methods for Ordinary Differential Equations by R.P. Kuzmina Pdf

In this book we consider a Cauchy problem for a system of ordinary differential equations with a small parameter. The book is divided into th ree parts according to three ways of involving the small parameter in the system. In Part 1 we study the quasiregular Cauchy problem. Th at is, a problem with the singularity included in a bounded function j , which depends on time and a small parameter. This problem is a generalization of the regu larly perturbed Cauchy problem studied by Poincare [35]. Some differential equations which are solved by the averaging method can be reduced to a quasiregular Cauchy problem. As an example, in Chapter 2 we consider the van der Pol problem. In Part 2 we study the Tikhonov problem. This is, a Cauchy problem for a system of ordinary differential equations where the coefficients by the derivatives are integer degrees of a small parameter.