Singular Perturbations Of Differential Operators

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Singular Perturbation Methods for Ordinary Differential Equations

Author : Robert E., Jr. O'Malley
Publisher : Springer Science & Business Media
ISBN 13 : 1461209773
Total Pages : 234 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Singular Perturbation Methods for Ordinary Differential Equations by : Robert E., Jr. O'Malley

Download or read book Singular Perturbation Methods for Ordinary Differential Equations written by Robert E., Jr. O'Malley and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book results from various lectures given in recent years. Early drafts were used for several single semester courses on singular perturbation meth ods given at Rensselaer, and a more complete version was used for a one year course at the Technische Universitat Wien. Some portions have been used for short lecture series at Universidad Central de Venezuela, West Vir ginia University, the University of Southern California, the University of California at Davis, East China Normal University, the University of Texas at Arlington, Universita di Padova, and the University of New Hampshire, among other places. As a result, I've obtained lots of valuable feedback from students and listeners, for which I am grateful. This writing continues a pattern. Earlier lectures at Bell Laboratories, at the University of Edin burgh and New York University, and at the Australian National University led to my earlier works (1968, 1974, and 1978). All seem to have been useful for the study of singular perturbations, and I hope the same will be true of this monograph. I've personally learned much from reading and analyzing the works of others, so I would especially encourage readers to treat this book as an introduction to a diverse and exciting literature. The topic coverage selected is personal and reflects my current opin ions. An attempt has been made to encourage a consistent method of ap proaching problems, largely through correcting outer limits in regions of rapid change. Formal proofs of correctness are not emphasized.

Singular Perturbations of Differential Operators

Author : Sergio Albeverio
Publisher : Cambridge University Press
ISBN 13 : 9780521779128
Total Pages : 454 pages
Book Rating : 4.7/5 (791 download)

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Book Synopsis Singular Perturbations of Differential Operators by : Sergio Albeverio

Download or read book Singular Perturbations of Differential Operators written by Sergio Albeverio and published by Cambridge University Press. This book was released on 2000-03-13 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a systematic mathematical study of differential (and more general self-adjoint) operators.

The Theory of Singular Perturbations

Author : E.M. de Jager
Publisher : Elsevier
ISBN 13 : 9780080542751
Total Pages : 339 pages
Book Rating : 4.5/5 (427 download)

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Book Synopsis The Theory of Singular Perturbations by : E.M. de Jager

Download or read book The Theory of Singular Perturbations written by E.M. de Jager and published by Elsevier. This book was released on 1996-11-08 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of this textbook is the mathematical theory of singular perturbations, which despite its respectable history is still in a state of vigorous development. Singular perturbations of cumulative and of boundary layer type are presented. Attention has been given to composite expansions of solutions of initial and boundary value problems for ordinary and partial differential equations, linear as well as quasilinear; also turning points are discussed. The main emphasis lies on several methods of approximation for solutions of singularly perturbed differential equations and on the mathematical justification of these methods. The latter implies a priori estimates of solutions of differential equations; this involves the application of Gronwall's lemma, maximum principles, energy integrals, fixed point theorems and Gåding's theorem for general elliptic equations. These features make the book of value to mathematicians and researchers in the engineering sciences, interested in the mathematical justification of formal approximations of solutions of practical perturbation problems. The text is selfcontained and each chapter is concluded with some exercises.

Singular Perturbations of Differential Operators

Author : Sergio Albeverio
Publisher :
ISBN 13 : 9781107089419
Total Pages : 446 pages
Book Rating : 4.0/5 (894 download)

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Book Synopsis Singular Perturbations of Differential Operators by : Sergio Albeverio

Download or read book Singular Perturbations of Differential Operators written by Sergio Albeverio and published by . This book was released on 2014-05-14 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a systematic mathematical study of differential (and more general self-adjoint) operators.

Algebraic Analysis of Singular Perturbation Theory

Author : Takahiro Kawai
Publisher : American Mathematical Soc.
ISBN 13 : 9780821835470
Total Pages : 148 pages
Book Rating : 4.8/5 (354 download)

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Book Synopsis Algebraic Analysis of Singular Perturbation Theory by : Takahiro Kawai

Download or read book Algebraic Analysis of Singular Perturbation Theory written by Takahiro Kawai and published by American Mathematical Soc.. This book was released on 2005 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: The topic of this book is the study of singular perturbations of ordinary differential equations, i.e., perturbations that represent solutions as asymptotic series rather than as analytic functions in a perturbation parameter. The main method used is the so-called WKB (Wentzel-Kramers-Brillouin) method, originally invented for the study of quantum-mechanical systems. The authors describe in detail the WKB method and its applications to the study of monodromy problems for Fuchsian differential equations and to the analysis of Painleve functions. This volume is suitable for graduate students and researchers interested in differential equations and special functions.

Methods and Applications of Singular Perturbations

Author : Ferdinand Verhulst
Publisher : Springer Science & Business Media
ISBN 13 : 0387283137
Total Pages : 332 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Methods and Applications of Singular Perturbations by : Ferdinand Verhulst

Download or read book Methods and Applications of Singular Perturbations written by Ferdinand Verhulst and published by Springer Science & Business Media. This book was released on 2006-06-04 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains well-chosen examples and exercises A student-friendly introduction that follows a workbook type approach

Singular Perturbations I

Author : L.S. Frank
Publisher : Elsevier
ISBN 13 : 9780080875446
Total Pages : 554 pages
Book Rating : 4.8/5 (754 download)

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Book Synopsis Singular Perturbations I by : L.S. Frank

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 Boundary Layers

Author : Gung-Min Gie
Publisher : Springer
ISBN 13 : 3030006387
Total Pages : 412 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Singular Perturbations and Boundary Layers by : Gung-Min Gie

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

Author : S. A. Lomov
Publisher : American Mathematical Soc.
ISBN 13 : 9780821897416
Total Pages : 402 pages
Book Rating : 4.8/5 (974 download)

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Book Synopsis Introduction to the General Theory of Singular Perturbations by : S. A. Lomov

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 and Differential Inequalities

Author : Frederick A. Howes
Publisher : American Mathematical Soc.
ISBN 13 : 0821818686
Total Pages : 83 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Singular Perturbations and Differential Inequalities by : Frederick A. Howes

Download or read book Singular Perturbations and Differential Inequalities written by Frederick A. Howes and published by American Mathematical Soc.. This book was released on 1976 with total page 83 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author discusses the singularly perturbed second-order boundary value problem [lowercase Greek]Epsilon [italic]y′′ = [italic]f([italic]t,[italic]y,[italic]y′, [lowercase Greek]Epsilon), by means of several second-order differential inequality theorems. This article not only gives a unified presentation of much of the body of results on this boundary value problem obtained in the last twenty years or so, but contains very considerable improvements involving less demanding conditions (sometimes leading to weaker results) in some cases, more precise results (sometimes under more severe restrictions) in other cases, and a more thorough investigation of the general boundary conditions. Some potential extensions to transition point problems and the like are indicated (but not carried out in detail) in the last section.

Singular Perturbations and Hysteresis

Author : Michael P. Mortell
Publisher : SIAM
ISBN 13 : 9780898717860
Total Pages : 357 pages
Book Rating : 4.7/5 (178 download)

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Book Synopsis Singular Perturbations and Hysteresis by : Michael P. Mortell

Download or read book Singular Perturbations and Hysteresis written by Michael P. Mortell and published by SIAM. This book was released on 2005-01-01 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together many important recent developments in the analysis of singular perturbation and hysteresis phenomena in an accessible and reasonably comprehensive fashion. To bridge a gap between practitioners of these phenomena, the editors conducted a workshop in April 2002 at University College Cork to provide a forum for experts in both fields 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.

Introduction to Singular Perturbations

Author : Robert E. Jr. O'Malley
Publisher : Elsevier
ISBN 13 : 0323162274
Total Pages : 215 pages
Book Rating : 4.3/5 (231 download)

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Book Synopsis Introduction to Singular Perturbations by : Robert E. Jr. O'Malley

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 215 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.

Singular Perturbation Methodology in Control Systems

Author : Desineni S. Naidu
Publisher : IET
ISBN 13 : 9780863411076
Total Pages : 314 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis Singular Perturbation Methodology in Control Systems by : Desineni S. Naidu

Download or read book Singular Perturbation Methodology in Control Systems written by Desineni S. Naidu and published by IET. This book was released on 1988 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the twin topics of singular perturbation methods and time scale analysis to problems in systems and control. The heart of the book is the singularly perturbed optimal control systems, which are notorious for demanding excessive computational costs. The book addresses both continuous control systems (described by differential equations) and discrete control systems (characterised by difference equations).

Singular Perturbations and Asymptotics

Author : Richard E. Meyer
Publisher : Academic Press
ISBN 13 : 1483264572
Total Pages : 418 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Singular Perturbations and Asymptotics by : Richard E. Meyer

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.

Multiple Scale and Singular Perturbation Methods

Author : J.K. Kevorkian
Publisher : Springer Science & Business Media
ISBN 13 : 1461239680
Total Pages : 642 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Multiple Scale and Singular Perturbation Methods by : J.K. Kevorkian

Download or read book Multiple Scale and Singular Perturbation Methods written by J.K. Kevorkian and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 642 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a revised and updated version, including a substantial portion of new material, of our text Perturbation Methods in Applied Mathematics (Springer Verlag, 1981). We present the material at a level that assumes some familiarity with the basics of ordinary and partial differential equations. Some of the more advanced ideas are reviewed as needed; therefore this book can serve as a text in either an advanced undergraduate course or a graduate-level course on the subject. Perturbation methods, first used by astronomers to predict the effects of small disturbances on the nominal motions of celestial bodies, have now become widely used analytical tools in virtually all branches of science. A problem lends itself to perturbation analysis if it is "close" to a simpler problem that can be solved exactly. Typically, this closeness is measured by the occurrence of a small dimensionless parameter, E, in the governing system (consisting of differential equations and boundary conditions) so that for E = 0 the resulting system is exactly solvable. The main mathematical tool used is asymptotic expansion with respect to a suitable asymptotic sequence of functions of E. In a regular perturbation problem, a straightforward procedure leads to a system of differential equations and boundary conditions for each term in the asymptotic expansion. This system can be solved recursively, and the accuracy of the result improves as E gets smaller, for all values of the independent variables throughout the domain of interest. We discuss regular perturbation problems in the first chapter.

Singular-Perturbation Theory

Author : Donald R. Smith
Publisher : Cambridge University Press
ISBN 13 : 9780521300421
Total Pages : 532 pages
Book Rating : 4.3/5 (4 download)

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Book Synopsis Singular-Perturbation Theory by : Donald R. Smith

Download or read book Singular-Perturbation Theory written by Donald R. Smith and published by Cambridge University Press. This book was released on 1985-08-30 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to singular perturbation problems. Since the nature of the nonuniformity can vary from case to case, the author considers and solves a variety of problems, mostly for ordinary differential equations.

hp-Finite Element Methods for Singular Perturbations

Author : Jens M. Melenk
Publisher : Springer
ISBN 13 : 354045781X
Total Pages : 326 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis hp-Finite Element Methods for Singular Perturbations by : Jens M. Melenk

Download or read book hp-Finite Element Methods for Singular Perturbations written by Jens M. Melenk and published by Springer. This book was released on 2004-10-20 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many partial differential equations arising in practice are parameter-dependent problems that are of singularly perturbed type. Prominent examples include plate and shell models for small thickness in solid mechanics, convection-diffusion problems in fluid mechanics, and equations arising in semi-conductor device modelling. Common features of these problems are layers and, in the case of non-smooth geometries, corner singularities. Mesh design principles for the efficient approximation of both features by the hp-version of the finite element method (hp-FEM) are proposed in this volume. For a class of singularly perturbed problems on polygonal domains, robust exponential convergence of the hp-FEM based on these mesh design principles is established rigorously.