Singular Perturbations and Asymptotics

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Publisher : Academic Press
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ISBN 10 : 9781483264578
Pages : 418 pages
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Rating : 4.4/5 (832 users download)


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Summary Book Review Singular Perturbations and Asymptotics :

Download or read book Singular Perturbations and Asymptotics written by Richard E. Meyer and published by Academic Press. This book was released on 2014-05-10 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics Research Center Symposia and Advanced Seminar Series: Singular Perturbations and Asymptotics covers the lectures presented at an Advanced Seminar on Singular Perturbation and Asymptotics, held in Madison, Wisconsin on May 28-30, 1980 under the auspices of the Mathematics Research Center of the University of Wisconsin—Madison. The book focuses on the processes, methodologies, reactions, and principles involved in singular perturbations and asymptotics, including boundary value problems, equations, perturbations, water waves, and gas dynamics. The selection first elaborates on basic concepts in the analysis of singular perturbations, limit process expansions and approximate equations, and results on singularly perturbed boundary value problems. Discussions focus on quasi-linear and nonlinear problems, semilinear systems, water waves, expansion in gas dynamics, asymptotic matching principles, and classical perturbation analysis. The text then takes a look at multiple solutions of singularly perturbed systems in the conditionally stable case and singular perturbations, stochastic differential equations, and applications. The book ponders on connection problems in the parameterless case; general connection-formula problem for linear differential equations of the second order; and turning-point problems for ordinary differential equations of hydrodynamic type. Topics include the comparison equation method, boundary layer flows, compound matrix method, asymptotic solution of the connection-formula problem, and higher order equations. The selection is a valuable source of information for researchers interested in singular perturbations and asymptotics.

Asymptotic Analysis of Singular Perturbations

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Publisher : Elsevier
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ISBN 10 : 0080875300
Pages : 286 pages
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Rating : 4.8/5 (753 users download)


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Summary Book Review Asymptotic Analysis of Singular Perturbations :

Download or read book Asymptotic Analysis of Singular Perturbations written by W. Eckhaus and published by Elsevier. This book was released on 2011-08-30 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: Asymptotic Analysis of Singular Perturbations

Asymptotic Methods and Singular Perturbations

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Publisher : American Mathematical Soc.
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ISBN 10 : 0821813307
Pages : 164 pages
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Summary Book Review Asymptotic Methods and Singular Perturbations :

Download or read book Asymptotic Methods and Singular Perturbations written by Robert E. O'Malley and published by American Mathematical Soc.. This book was released on 1976 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Matched Asymptotic Expansions and Singular Perturbations

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Publisher : Elsevier
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ISBN 10 : 9780080871172
Pages : 144 pages
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Summary Book Review Matched Asymptotic Expansions and Singular Perturbations :

Download or read book Matched Asymptotic Expansions and Singular Perturbations written by and published by Elsevier. This book was released on 2011-08-26 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: Matched Asymptotic Expansions and Singular Perturbations

Singular Perturbations and Asymptotic Analysis in Control Systems

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Publisher : Springer Verlag
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ISBN 10 : UCAL:B4405877
Pages : 432 pages
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Summary Book Review Singular Perturbations and Asymptotic Analysis in Control Systems :

Download or read book Singular Perturbations and Asymptotic Analysis in Control Systems written by Petar V. Kokotović and published by Springer Verlag. This book was released on 1987 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Singular Perturbation Theory

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Publisher : Springer
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ISBN 10 : 1441999574
Pages : 85 pages
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Summary Book Review Singular Perturbation Theory :

Download or read book Singular Perturbation Theory written by Lindsay A. Skinner and published by Springer. This book was released on 2011-05-18 with total page 85 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Boundary Function Method for Singular Perturbed Problems

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Publisher : SIAM
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ISBN 10 : 1611970784
Pages : 234 pages
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Summary Book Review The Boundary Function Method for Singular Perturbed Problems :

Download or read book The Boundary Function Method for Singular Perturbed Problems written by Adelaida B. Vasil'eva and published by SIAM. This book was released on 1995-01-01 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book published in English devoted solely to the boundary function method, which is one of the asymptotic methods. This method provides an effective and simple way to obtain asymptotic approximations for the solutions of certain ordinary and partial differential equations containing small parameters in front of the highest derivatives. These equations, called singularly perturbed equations, are often used in modeling. In addition to numerous examples, the book includes discussions on singularly perturbed problems from chemical kinetics and heat conduction, semiconductor device modeling, and mathematical biology. The book also contains a variety of original ideas and explicit calculations previously available only in journal literature, as well as many concrete applied problems illustrating the boundary function method algorithms. Quite general asymptotic results described in the book are rigorous in the sense that, along with the asymptotic algorithms, in most cases the theorems on estimation of the remainder terms are presented. A survey of results of Russian mathematicians on the subject is provided; many of these results are not well known in the West. Based on the Russian edition of the textbook by Vasil'eva and Butuzov, this American edition, prepared by Kalachev, differs in many aspects. The text of the book has been revised substantially, some new material has been added to every chapter, and more examples, exercises, and new references on asymptotic methods and their applications have been included.

Introduction to Singular Perturbations

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Publisher : Elsevier
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ISBN 10 : 9780323162272
Pages : 214 pages
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Rating : 4.3/5 (231 users download)


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Summary Book Review Introduction to Singular Perturbations :

Download or read book Introduction to Singular Perturbations written by Robert E. Jr. O'Malley and published by Elsevier. This book was released on 2012-12-02 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Singular Perturbations provides an overview of the fundamental techniques for obtaining asymptomatic solutions to boundary value problems. This text explores singular perturbation techniques, which are among the basic tools of several applied scientists. This book is organized into eight chapters, wherein Chapter 1 discusses the method of matched asymptomatic expansions, which has been frequently applied to several physical problems involving singular perturbations. Chapter 2 considers the nonlinear initial value problem to illustrate the regular perturbation method, and Chapter 3 explains how to construct asymptotic solutions for general linear equations. Chapter 4 discusses scalar equations and nonlinear system, whereas Chapters 5 and 6 explain the contrasts for initial value problems where the outer expansion cannot be determined without obtaining the initial values of the boundary layer correction. Chapters 7 and 8 deal with boundary value problem that arises in the study of adiabatic tubular chemical flow reactors with axial diffusion. This monograph is a valuable resource for applied mathematicians, engineers, researchers, students, and readers whose interests span a variety of fields.

Asymptotic Analysis of Singular Perturbations

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Publisher : Elsevier Science Limited
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ISBN 10 : UCAL:B4406388
Pages : 308 pages
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Summary Book Review Asymptotic Analysis of Singular Perturbations :

Download or read book Asymptotic Analysis of Singular Perturbations written by Wiktor Eckhaus and published by Elsevier Science Limited. This book was released on 1979 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: Asymptotic Analysis of Singular Perturbations.

Lecture Notes on Mean Curvature Flow: Barriers and Singular Perturbations

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Publisher : Springer
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ISBN 10 : 9788876424298
Pages : 329 pages
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Summary Book Review Lecture Notes on Mean Curvature Flow: Barriers and Singular Perturbations :

Download or read book Lecture Notes on Mean Curvature Flow: Barriers and Singular Perturbations written by Giovanni Bellettini and published by Springer. This book was released on 2014-05-13 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the book is to study some aspects of geometric evolutions, such as mean curvature flow and anisotropic mean curvature flow of hypersurfaces. We analyze the origin of such flows and their geometric and variational nature. Some of the most important aspects of mean curvature flow are described, such as the comparison principle and its use in the definition of suitable weak solutions. The anisotropic evolutions, which can be considered as a generalization of mean curvature flow, are studied from the view point of Finsler geometry. Concerning singular perturbations, we discuss the convergence of the Allen–Cahn (or Ginsburg–Landau) type equations to (possibly anisotropic) mean curvature flow before the onset of singularities in the limit problem. We study such kinds of asymptotic problems also in the static case, showing convergence to prescribed curvature-type problems.

Asymptotic Behavior of Monodromy

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Publisher : Springer
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ISBN 10 : 3540550097
Pages : 142 pages
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Summary Book Review Asymptotic Behavior of Monodromy :

Download or read book Asymptotic Behavior of Monodromy written by Carlos Simpson and published by Springer. This book was released on 1991-12-11 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book concerns the question of how the solution of a system of ODE's varies when the differential equation varies. The goal is to give nonzero asymptotic expansions for the solution in terms of a parameter expressing how some coefficients go to infinity. A particular classof families of equations is considered, where the answer exhibits a new kind of behavior not seen in most work known until now. The techniques include Laplace transform and the method of stationary phase, and a combinatorial technique for estimating the contributions of terms in an infinite series expansion for the solution. Addressed primarily to researchers inalgebraic geometry, ordinary differential equations and complex analysis, the book will also be of interest to applied mathematicians working on asymptotics of singular perturbations and numerical solution of ODE's.

Singular Perturbation Theory

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Publisher : Springer Science & Business Media
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ISBN 10 : 9780387232171
Pages : 292 pages
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Summary Book Review Singular Perturbation Theory :

Download or read book Singular Perturbation Theory written by R.S. Johnson and published by Springer Science & Business Media. This book was released on 2006-01-16 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: The importance of mathematics in the study of problems arising from the real world, and the increasing success with which it has been used to model situations ranging from the purely deterministic to the stochastic, is well established. The purpose of the set of volumes to which the present one belongs is to make available authoritative, up to date, and self-contained accounts of some of the most important and useful of these analytical approaches and techniques. Each volume provides a detailed introduction to a specific subject area of current importance that is summarized below, and then goes beyond this by reviewing recent contributions, and so serving as a valuable reference source. The progress in applicable mathematics has been brought about by the extension and development of many important analytical approaches and techniques, in areas both old and new, frequently aided by the use of computers without which the solution of realistic problems would otherwise have been impossible.

Singular Perturbations and Boundary Layers

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Publisher : Springer
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ISBN 10 : 9783030006389
Pages : 412 pages
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Summary Book Review Singular Perturbations and Boundary Layers :

Download or read book Singular Perturbations and Boundary Layers written by Gung-Min Gie and published by Springer. This book was released on 2018-11-21 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: Singular perturbations occur when a small coefficient affects the highest order derivatives in a system of partial differential equations. From the physical point of view singular perturbations generate in the system under consideration thin layers located often but not always at the boundary of the domains that are called boundary layers or internal layers if the layer is located inside the domain. Important physical phenomena occur in boundary layers. The most common boundary layers appear in fluid mechanics, e.g., the flow of air around an airfoil or a whole airplane, or the flow of air around a car. Also in many instances in geophysical fluid mechanics, like the interface of air and earth, or air and ocean. This self-contained monograph is devoted to the study of certain classes of singular perturbation problems mostly related to thermic, fluid mechanics and optics and where mostly elliptic or parabolic equations in a bounded domain are considered. This book is a fairly unique resource regarding the rigorous mathematical treatment of boundary layer problems. The explicit methodology developed in this book extends in many different directions the concept of correctors initially introduced by J. L. Lions, and in particular the lower- and higher-order error estimates of asymptotic expansions are obtained in the setting of functional analysis. The review of differential geometry and treatment of boundary layers in a curved domain is an additional strength of this book. In the context of fluid mechanics, the outstanding open problem of the vanishing viscosity limit of the Navier-Stokes equations is investigated in this book and solved for a number of particular, but physically relevant cases. This book will serve as a unique resource for those studying singular perturbations and boundary layer problems at the advanced graduate level in mathematics or applied mathematics and may be useful for practitioners in other related fields in science and engineering such as aerodynamics, fluid mechanics, geophysical fluid mechanics, acoustics and optics.

Introduction to the General Theory of Singular Perturbations

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Publisher : American Mathematical Soc.
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ISBN 10 : 0821897411
Pages : 402 pages
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Summary Book Review Introduction to the General Theory of Singular Perturbations :

Download or read book Introduction to the General Theory of Singular Perturbations written by S. A. Lomov and published by American Mathematical Soc.. This book was released on with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is aimed at researchers and students in physics, mathematics, and engineering. It contains the first systematic presentation of a general approach to the integration of singularly perturbed differential equations describing nonuniform transitions, such as the occurrence of a boundary layer, discontinuities, boundary effects and so on. The method of regularization of singular perturbations presented here can be applied to the asymptotic integration of systems of ordinary and partial differential equations.

Singular Perturbations I

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Publisher : Elsevier
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ISBN 10 : 0080875440
Pages : 554 pages
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Summary Book Review Singular Perturbations I :

Download or read book Singular Perturbations I written by L.S. Frank and published by Elsevier. This book was released on 1990-08-16 with total page 554 pages. Available in PDF, EPUB and Kindle. Book excerpt: Singular perturbations, one of the central topics in asymptotic analysis, also play a special role in describing physical phenomena such as the propagation of waves in media in the presence of small energy dissipations or dispersions, the appearance of boundary or interior layers in fluid and gas dynamics, as well as in elasticity theory, semi-classical asymptotic approximations in quantum mechanics etc. Elliptic and coercive singular perturbations are of special interest for the asymptotic solution of problems which are characterized by boundary layer phenomena, e.g. the theory of thin buckling plates, elastic rods and beams. This first volume deals with linear singular perturbations (on smooth manifolds without boundary) considered as equicontinuous linear mappings between corresponding families of Sobolev-Slobodetski's type spaces of vectorial order.

Singular Perturbations and Asymptotics

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ISBN 10 : 0124932606
Pages : 432 pages
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Rating : 4.9/5 (326 users download)


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Summary Book Review Singular Perturbations and Asymptotics :

Download or read book Singular Perturbations and Asymptotics written by Richard E. Meyer and published by . This book was released on 1980 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of an advanced seminar on Singular Perturbations and Asymptotics in Madison, Wisconsin on May 28-30, 1980 under the auspices of the Mathematics Research Center of the The University of Wisconsin-Madison, sponsored by the United States Army and supported by the Office of Naval Research. The subject of singular perturbations, not to mention asymptotics, is too large for a single conference, and the selection of topics reflects areas of recent research activity and advances.

Singular Perturbation and Hysteresis

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Publisher : Cambridge University Press
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ISBN 10 : 0898715970
Pages : 362 pages
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Rating : 4.7/5 (159 users download)


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Summary Book Review Singular Perturbation and Hysteresis :

Download or read book Singular Perturbation and Hysteresis written by Alexei Pokrovskii and published by Cambridge University Press. This book was released on 2005-06 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book unifies many important recent developments in the analysis of singular perturbation and hysteresis phenomena in an accessible and comprehensive fashion. In April 2002 at University College Cork in Ireland, the editors conducted a workshop to provide a forum for experts to share their interests and knowledge. For this book, the editors have compiled research from those practitioners in areas such as reacting systems, semiconductor lasers, shock phenomena in economic modeling, and fluid mechanics, all with an emphasis on hysteresis and singular perturbations. A basic introduction to hysteresis and singular perturbation theory is included, with simple examples from both physics and mathematics. Later chapters address: applications of hysteresis to economics; various aspects of the asymptotic theory of singularly perturbed systems; typical problems of the asymptotic theory of contrast structures; and the geometrical approach to an investigation of models with singular perturbations and hysteresis.