Matched Asymptotic Expansions

Author : P.A. Lagerstrom
Publisher : Springer Science & Business Media
Page : 263 pages
File Size : 52,9 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475719901

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Matched Asymptotic Expansions by P.A. Lagerstrom Pdf

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 : Anonim
Publisher : Elsevier
Page : 144 pages
File Size : 53,8 Mb
Release : 2011-08-26
Category : Mathematics
ISBN : 9780080871172

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Matched Asymptotic Expansions and Singular Perturbations by Anonim Pdf

Matched Asymptotic Expansions and Singular Perturbations

Author : Augustin Fruchard,Reinhard Schafke
Publisher : Springer
Page : 161 pages
File Size : 55,8 Mb
Release : 2012-12-15
Category : Mathematics
ISBN : 9783642340352

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Composite Asymptotic Expansions by Augustin Fruchard,Reinhard Schafke Pdf

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
Page : 385 pages
File Size : 46,7 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 : M.V. Fedoryuk
Publisher : Springer Science & Business Media
Page : 248 pages
File Size : 46,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642584237

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Partial Differential Equations V by M.V. Fedoryuk Pdf

In this paper we shall discuss the construction of formal short-wave asymp totic solutions of problems of mathematical physics. The topic is very broad. It can somewhat conveniently be divided into three parts: 1. Finding the short-wave asymptotics of a rather narrow class of problems, which admit a solution in an explicit form, via formulas that represent this solution. 2. Finding formal asymptotic solutions of equations that describe wave processes by basing them on some ansatz or other. We explain what 2 means. Giving an ansatz is knowing how to give a formula for the desired asymptotic solution in the form of a series or some expression containing a series, where the analytic nature of the terms of these series is indicated up to functions and coefficients that are undetermined at the first stage of consideration. The second stage is to determine these functions and coefficients using a direct substitution of the ansatz in the equation, the boundary conditions and the initial conditions. Sometimes it is necessary to use different ansiitze in different domains, and in the overlapping parts of these domains the formal asymptotic solutions must be asymptotically equivalent (the method of matched asymptotic expansions). The basis for success in the search for formal asymptotic solutions is a suitable choice of ansiitze. The study of the asymptotics of explicit solutions of special model problems allows us to "surmise" what the correct ansiitze are for the general solution.

Author : P. A. Lagerstrom
Publisher : Unknown
Page : 270 pages
File Size : 48,7 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 1475719914

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Matched Asymptotic Expansions by P. A. Lagerstrom Pdf

Author : J.A. Leach,D.J. Needham
Publisher : Springer Science & Business Media
Page : 290 pages
File Size : 41,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9780857293961

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Matched Asymptotic Expansions in Reaction-Diffusion Theory by J.A. Leach,D.J. Needham Pdf

This volume contains a wealth of results and methodologies applicable to a wide range of problems arising in reaction-diffusion theory. It can be viewed both as a handbook, and as a detailed description of the methodology. The authors present new methods based on matched asymptotic expansions.

Author : A. M. Ilʹin
Publisher : American Mathematical Soc.
Page : 281 pages
File Size : 45,8 Mb
Release : 1992
Category : Mathematics
ISBN : 0821845616

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Matching of Asymptotic Expansions of Solutions of Boundary Value Problems by A. M. Ilʹin Pdf

This book deals with the solution of singularly perturbed boundary value problems for differential equations. It presents, for the first time, a detailed and systematic treatment of the version of the matching method developed by the author and his colleagues. A broad class of problems is considered from a unified point of view, and the procedure for constructing asymptotic expansions is discussed in detail. The book covers formal constructions of asymptotic expansions and provides rigorous justifications of these asymptotics. One highlight is a complete asymptotic analysis of Burger's equation with small diffusion in the neighborhood of the gradient catastrophe point. The book is suitable as a text for graduate study in asymptotic methods in calculus and singularly perturbed equations.

Author : Jean Cousteix,Jacques Mauss
Publisher : Springer Science & Business Media
Page : 437 pages
File Size : 55,6 Mb
Release : 2007-03-22
Category : Science
ISBN : 9783540464891

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Asymptotic Analysis and Boundary Layers by Jean Cousteix,Jacques Mauss Pdf

This book presents a new method of asymptotic analysis of boundary-layer problems, the Successive Complementary Expansion Method (SCEM). The first part is devoted to a general presentation of the tools of asymptotic analysis. It gives the keys to understand a boundary-layer problem and explains the methods to construct an approximation. The second part is devoted to SCEM and its applications in fluid mechanics, including external and internal flows.

Author : F. Verhulst
Publisher : Springer
Page : 249 pages
File Size : 47,6 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540353324

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Asymptotic Analysis by F. Verhulst Pdf

Author : J. A. Leach,D. J. Needham
Publisher : Unknown
Page : 304 pages
File Size : 40,5 Mb
Release : 2003-11-01
Category : Electronic
ISBN : 0857293974

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Matched Asymptotic Expansions in Reaction-Diffusion Theory by J. A. Leach,D. J. Needham Pdf

Author : Robert E. O'Malley
Publisher : Springer
Page : 256 pages
File Size : 51,9 Mb
Release : 2014-11-19
Category : Mathematics
ISBN : 9783319119243

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Historical Developments in Singular Perturbations by Robert E. O'Malley Pdf

This engaging text describes the development of singular perturbations, including its history, accumulating literature, and its current status. While the approach of the text is sophisticated, the literature is accessible to a broad audience. A particularly valuable bonus are the historical remarks. These remarks are found throughout the manuscript. They demonstrate the growth of mathematical thinking on this topic by engineers and mathematicians. The book focuses on detailing how the various methods are to be applied. These are illustrated by a number and variety of examples. Readers are expected to have a working knowledge of elementary ordinary differential equations, including some familiarity with power series techniques, and of some advanced calculus. Dr. O'Malley has written a number of books on singular perturbations. This book has developed from many of his works in the field of perturbation theory.

Author : E. J. Hinch
Publisher : Cambridge University Press
Page : 178 pages
File Size : 42,7 Mb
Release : 1991-10-25
Category : Mathematics
ISBN : 0521378974

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Perturbation Methods by E. J. Hinch Pdf

A textbook presenting the theory and underlying techniques of perturbation methods in a manner suitable for senior undergraduates from a broad range of disciplines.

Author : Mark H. Holmes
Publisher : Springer Science & Business Media
Page : 344 pages
File Size : 47,8 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461253471

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Introduction to Perturbation Methods by Mark H. Holmes Pdf

This introductory graduate text is based on a graduate course the author has taught repeatedly over the last ten years to students in applied mathematics, engineering sciences, and physics. Each chapter begins with an introductory development involving ordinary differential equations, and goes on to cover such traditional topics as boundary layers and multiple scales. However, it also contains material arising from current research interest, including homogenisation, slender body theory, symbolic computing, and discrete equations. Many of the excellent exercises are derived from problems of up-to-date research and are drawn from a wide range of application areas.

Author : Lindsay A. Skinner
Publisher : Springer Science & Business Media
Page : 85 pages
File Size : 43,6 Mb
Release : 2011-05-11
Category : Mathematics
ISBN : 9781441999580

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Singular Perturbation Theory by Lindsay A. Skinner Pdf

This book is a rigorous presentation of the method of matched asymptotic expansions, the primary tool for attacking singular perturbation problems. A knowledge of conventional asymptotic analysis is assumed. The first chapter introduces the theory and is followed by four chapters of applications to ordinary differential equation problems of increasing complexity. Exercises are included as well as several Maple programs for computing the terms of the various asymptotic expansions that arise in solving the problems.