Perturbation Methods

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: E. J. Hinch

Publisher: Cambridge University Press

ISBN: 9780521378970

Category: Mathematics

Page: 160

View: 222

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

Introduction to Perturbation Methods

The latter are intended to provide a window into the wide range of areas that use
perturbation methods. Solutions to some of the exercises are available from the
author's home page located at http://www.math.rpi.edu/~holmes. Also located ...

Author: Mark H. Holmes

Publisher: Springer Science & Business Media

ISBN: 9780387942032

Category: Mathematics

Page: 356

View: 545

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.

Perturbation Methods Instability Catastrophe and Chaos

CHAPTER 2 PERTURBATION METHODS 2.1 REGULAR AND SINGULAR
PERTURBATION Many of the differential equations that are of interest to
engineers and scientists cannot be solved exactly . In Chapter 1 , we have
explained methods ...

Author: Wenfang Chen

Publisher: World Scientific

ISBN: 9789810237271

Category: Mathematics

Page: 260

View: 601

This important book introduces perturbation and qualitative methods for differential equations in terms understandable to students with only a basic knowledge of calculus and ordinary linear differential equations. Theorems are stated clearly with their limitations and restrictions and are applied to solve examples from various disciplines. The writing style is informal and new ideas are introduced gradually via concepts already familiar to the reader.

Analyzing Multiscale Phenomena Using Singular Perturbation Methods

Introduction to geometric methods and dynamical system theory for singular
perturbation problems, these proceedings (1998). 23. J.K. Kevorkian and J.D.
Cole, Multiple Scales and Singular Perturbation Methods, Springer- Verlag, New
York, ...

Author: Jane Cronin

Publisher: American Mathematical Soc.

ISBN: 9780821867617

Category: Mathematics

Page: 187

View: 170

To understand multiscale phenomena, it is essential to employ asymptotic methods to construct approximate solutions and to design effective computational algorithms. This volume consists of articles based on the AMS Short Course in Singular Perturbations held at the annual Joint Mathematics Meetings in Baltimore (MD). Leading experts discussed the following topics which they expand upon in the book: boundary layer theory, matched expansions, multiple scales, geometric theory, computational techniques, and applications in physiology and dynamic metastability. Readers will find that this text offers an up-to-date survey of this important field with numerous references to the current literature, both pure and applied.

Multiple Scale and Singular Perturbation Methods

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).

Author: J.K. Kevorkian

Publisher: Springer Science & Business Media

ISBN: 1461239680

Category: Mathematics

Page: 634

View: 997

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.

Perturbation Methods

Currently available in the Series: T. W. Anderson The Statistical Analysis of Time Series T. S. Arthanari & Yadolah Dodge Mathematical Programming in Statistics Emil Artin Geometric Algebra Norman T. J. Bailey The Elements of Stochastic ...

Author: Ali H. Nayfeh

Publisher: John Wiley & Sons

ISBN: 3527617612

Category: Science

Page: 437

View: 761

The Wiley Classics Library consists of selected books that have become recognized classics in their respective fields. With these new unabridged and inexpensive editions, Wiley hopes to extend the life of these important works by making them available to future generations of mathematicians and scientists. Currently available in the Series: T. W. Anderson The Statistical Analysis of Time Series T. S. Arthanari & Yadolah Dodge Mathematical Programming in Statistics Emil Artin Geometric Algebra Norman T. J. Bailey The Elements of Stochastic Processes with Applications to the Natural Sciences Robert G. Bartle The Elements of Integration and Lebesgue Measure George E. P. Box & Norman R. Draper Evolutionary Operation: A Statistical Method for Process Improvement George E. P. Box & George C. Tiao Bayesian Inference in Statistical Analysis R. W. Carter Finite Groups of Lie Type: Conjugacy Classes and Complex Characters R. W. Carter Simple Groups of Lie Type William G. Cochran & Gertrude M. Cox Experimental Designs, Second Edition Richard Courant Differential and Integral Calculus, Volume I RIchard Courant Differential and Integral Calculus, Volume II Richard Courant & D. Hilbert Methods of Mathematical Physics, Volume I Richard Courant & D. Hilbert Methods of Mathematical Physics, Volume II D. R. Cox Planning of Experiments Harold S. M. Coxeter Introduction to Geometry, Second Edition Charles W. Curtis & Irving Reiner Representation Theory of Finite Groups and Associative Algebras Charles W. Curtis & Irving Reiner Methods of Representation Theory with Applications to Finite Groups and Orders, Volume I Charles W. Curtis & Irving Reiner Methods of Representation Theory with Applications to Finite Groups and Orders, Volume II Cuthbert Daniel Fitting Equations to Data: Computer Analysis of Multifactor Data, Second Edition Bruno de Finetti Theory of Probability, Volume I Bruno de Finetti Theory of Probability, Volume 2 W. Edwards Deming Sample Design in Business Research

Perturbation Methods in the Computer Age

It lists many of the most important books written on asymptotic theory and
perturbation methods . Thus , the primary goal of this book is to provide a
practical and understandable introduction to the intriguing field of asymptotic
methods . Chapter ...

Author: David C. Wilcox

Publisher: D C W Industries

ISBN:

Category: Asymptotic expansions

Page: 224

View: 463


Perturbation Methods in Heat Transfer

A. Aziz, T. Y. Na. Io PERTURBATION METHODS IN HEAT TRANSFER Series in
Computational Methods in.

Author: A. Aziz

Publisher: Hemisphere Pub

ISBN:

Category: Technology & Engineering

Page: 199

View: 835


Perturbation Methods in Optimal Control

Author: Alain Bensoussan

Publisher: Wiley

ISBN: 9780471919940

Category: Mathematics

Page: 588

View: 842

Describes, analyzes, and generalizes the principal results concerning perturbation methods in optimal control for systems governed by deterministic or stochastic differential equations. Covers the most important theorems in deterministic and stochastic optimal control, the theory of ergodic control, and the use of control, including regular perturbations and singular perturbations.

Lie Transforms and Perturbation Methods

Author: Jack S. Griffith

Publisher:

ISBN:

Category: Lie groups

Page: 123

View: 770


Perturbation Methods and Semilinear Elliptic Problems on R n

In some other circ- stances, one studies perturbations either because this is the ?rst step to obtain global results or else because it often provides a correct perspective for further global studies.

Author: Antonio Ambrosetti

Publisher: Springer Science & Business Media

ISBN: 3764373962

Category: Mathematics

Page: 184

View: 259

Several important problems arising in Physics, Di?erential Geometry and other n topics lead to consider semilinear variational elliptic equations on R and a great deal of work has been devoted to their study. From the mathematical point of view, the main interest relies on the fact that the tools of Nonlinear Functional Analysis, based on compactness arguments, in general cannot be used, at least in a straightforward way, and some new techniques have to be developed. n On the other hand, there are several elliptic problems on R which are p- turbative in nature. In some cases there is a natural perturbation parameter, like inthe bifurcationfromthe essentialspectrum orinsingularlyperturbed equations or in the study of semiclassical standing waves for NLS. In some other circ- stances, one studies perturbations either because this is the ?rst step to obtain global results or else because it often provides a correct perspective for further global studies. For these perturbation problems a speci?c approach,that takes advantage of such a perturbative setting, seems the most appropriate. These abstract tools are provided by perturbation methods in critical point theory. Actually, it turns out that such a framework can be used to handle a large variety of equations, usually considered di?erent in nature. Theaimofthismonographistodiscusstheseabstractmethodstogetherwith their applications to several perturbation problems, whose common feature is to n involve semilinear Elliptic Partial Di?erential Equations on R with a variational structure.

Nonlinear Zero sum Differential Game Analysis by Singular Perturbation Methods

The singular-perturbation parameters in this problem are the ratio of the turning
radii of the players to the initial distance of separation. The approximate strategy
pair for this game, obtained by using the singular-perturbation technique, is given
 ...

Author:

Publisher:

ISBN:

Category:

Page: 30

View: 347


The Application of Perturbation Methods to the Theory of Nuclear Matter

COUNOD Y TRA EZRA IND Cornell University Library 10788 1958 T55 The
application of perturbation methods By LIBRARY มั่น 02 CORNELI CORREU
LOURDE UNTVO LIBRARY CORNEL CORNELL ORNELE COUNDED Yo123 3
1924 ...

Author: David James Thouless

Publisher:

ISBN:

Category: Nuclear physics

Page: 172

View: 490


Applications of Regular and Singular Perturbation Methods in Beam Problems

APPLICATIONS OF REGULAR AND SINGULAR PERTURBATION METHODS IN
BEAM PROBLEMS A Thesis Presented to the Facility of the Graduate School of
Cornell University for the Degree of Master of Science hy Kolumban Hutter June
 ...

Author: Kolumban Hutter

Publisher:

ISBN:

Category: Girders

Page: 106

View: 103


Singular Perturbation Methods for Ordinary Differential Equations

Author: Robert E., Jr. O'Malley

Publisher: Springer

ISBN: 9780387975566

Category: Mathematics

Page: 227

View: 764

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.

Hybrid Computer Simulation Techniques and Perturbation Methods of Analysis for the Study of DC Power Transmission Systems

TITLE OF THESIS - - - - Hybrid Computer Simulation Techniques And
Perturbation - - Methods of Analysis for the Study of DC Power Transmission
Systems Full Name - - - - - - - - - - - Dennis Patrick Carroll Place and Date of Birth -
- Minneapolis ...

Author: Dennis Patrick Carroll

Publisher:

ISBN:

Category: Electric power distribution

Page: 322

View: 204


An Asymptotic Formulation of Canonical Perturbation Methods and Applications to Satellite Theory

Author: John Mark Gormally

Publisher:

ISBN:

Category: Perturbation (Astronomy)

Page: 646

View: 427


Introduction to Perturbation Methods

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.

Author: Mark H. Holmes

Publisher: Springer Science & Business Media

ISBN: 1461253470

Category: Mathematics

Page: 356

View: 362

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.

Perturbation Methods in Applied Mathematics

This book is a revised and updated version, including a substantial portion of new material, of J. D. Cole's text Perturbation Methods in Applied Mathe matics, Ginn-Blaisdell, 1968.

Author: J. Kevorkian

Publisher: Springer Science & Business Media

ISBN: 1475742134

Category: Mathematics

Page: 560

View: 442

This book is a revised and updated version, including a substantial portion of new material, of J. D. Cole's text Perturbation Methods in Applied Mathe matics, Ginn-Blaisdell, 1968. We present the material at a level which 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. The applied mathematician, attempting to understand or solve a physical problem, very often uses a perturbation procedure. In doing this, he usually draws on a backlog of experience gained from the solution of similar examples rather than on some general theory of perturbations. The aim of this book is to survey these perturbation methods, especially in connection with differ ential equations, in order to illustrate certain general features common to many examples. The basic ideas, however, are also applicable to integral equations, integrodifferential equations, and even to_difference equations. In essence, a perturbation procedure consists of constructing the solution for a problem involving a small parameter B, either in the differential equation or the boundary conditions or both, when the solution for the limiting case B = 0 is known. The main mathematical tool used is asymptotic expansion with respect to a suitable asymptotic sequence of functions of B.

Random Perturbation Methods with Applications in Science and Engineering

This book develops methods for describing random dynamical systems, and it illustrats how the methods can be used in a variety of applications.

Author: Anatoli V. Skorokhod

Publisher: Springer Science & Business Media

ISBN: 0387224467

Category: Mathematics

Page: 490

View: 99

This book develops methods for describing random dynamical systems, and it illustrats how the methods can be used in a variety of applications. Appeals to researchers and graduate students who require tools to investigate stochastic systems.