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Author : W. Eckhaus
Publisher : Elsevier
Page : 286 pages
File Size : 55,8 Mb
Release : 2011-08-30
Category : Mathematics
ISBN : 0080875300
Asymptotic Analysis of Singular Perturbations
Author : Anonim
Publisher : Elsevier
Page : 144 pages
File Size : 55,6 Mb
Release : 2011-08-26
Category : Mathematics
ISBN : 9780080871172
Matched Asymptotic Expansions and Singular Perturbations
Author : Desineni S. Naidu
Publisher : IET
Page : 314 pages
File Size : 40,5 Mb
Release : 1988
Category : Technology & Engineering
ISBN : 086341107X
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).
Author : Lindsay A. Skinner
Publisher : Springer Science & Business Media
Page : 85 pages
File Size : 52,5 Mb
Release : 2011-05-11
Category : Mathematics
ISBN : 9781441999580
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.
Author : Takahiro Kawai,Yoshitsugu Takei
Publisher : American Mathematical Soc.
Page : 148 pages
File Size : 52,9 Mb
Release : 2005
Category : Mathematics
ISBN : 0821835475
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.
Author : Petar V. Kokotovic,Alain Bensoussan,Gilmer L. Blankenship
Publisher : Springer
Page : 432 pages
File Size : 54,9 Mb
Release : 1987-02-27
Category : Language Arts & Disciplines
ISBN : UCAL:B4405877
Author : S. A. Lomov
Publisher : American Mathematical Soc.
Page : 402 pages
File Size : 46,9 Mb
Release : 2024-06-15
Category : Mathematics
ISBN : 0821897411
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.
Author : Robert E. Jr. O'Malley
Publisher : Elsevier
Page : 215 pages
File Size : 52,8 Mb
Release : 2012-12-02
Category : Mathematics
ISBN : 9780323162272
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.
Author : Robert E. O'Malley
Publisher : American Mathematical Soc.
Page : 164 pages
File Size : 53,7 Mb
Release : 1976
Category : Mathematics
ISBN : 0821813307
Author : L.S. Frank
Publisher : Elsevier
Page : 554 pages
File Size : 50,5 Mb
Release : 1990-08-16
Category : Mathematics
ISBN : 0080875440
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.
Author : W. Eckhaus,E.M. de Jager
Publisher : Springer
Page : 371 pages
File Size : 50,9 Mb
Release : 2007-01-05
Category : Mathematics
ISBN : 9783540393320
Author : Michael P. Mortell,Robert E. O'Malley,Alexei Pokrovskii,Vladimir Sobolev
Publisher : SIAM
Page : 356 pages
File Size : 47,6 Mb
Release : 2005-06-01
Category : Mathematics
ISBN : 9780898715972
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.
Author : Richard E. Meyer,Seymour V. Parter
Publisher : Academic Press
Page : 418 pages
File Size : 49,9 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483264578
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.
Author : Robert E., Jr. O'Malley
Publisher : Springer Science & Business Media
Page : 234 pages
File Size : 51,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461209775
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.
Author : J.K. Kevorkian,J.D. Cole
Publisher : Springer Science & Business Media
Page : 642 pages
File Size : 51,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461239680
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.
