Multiple Scale And Singular Perturbation Methods

Author : J K Kevorkian,J D Cole
Publisher : Unknown
Page : 646 pages
File Size : 55,8 Mb
Release : 1996-05-15
Category : Electronic
ISBN : 1461239699

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Multiple Scale and Singular Perturbation Methods by J K Kevorkian,J D Cole Pdf

This book is a revised and updated version, including a substantial portion of new material, of the authors' widely acclaimed earlier text "Perturbation Methods in Applied Mathematics." A new chapter dealing with regular expansions has been added, the discussion of layer-type singular perturbations has been revised, and the coverage of multiple scale and averaging methods has been significantly expanded to reflect recent advances and viewpoints. The result is a comprehensive account of the various perturbation techniques currently used in the sciences and engineering, and is suitable for a graduate text as well as a reference work on the subject.

Author : J.K. Kevorkian,J.D. Cole
Publisher : Springer Science & Business Media
Page : 642 pages
File Size : 51,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461239680

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Multiple Scale and Singular Perturbation Methods by J.K. Kevorkian,J.D. Cole Pdf

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.

Author : J. Kevorkian,J. D. Cole
Publisher : Unknown
Page : 640 pages
File Size : 46,8 Mb
Release : 1996-06-30
Category : Electronic
ISBN : 3540942025

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Multiple Scale and Singular Perturbation Methods by J. Kevorkian,J. D. Cole Pdf

Author : Jane Cronin
Publisher : American Mathematical Soc.
Page : 201 pages
File Size : 43,5 Mb
Release : 1999
Category : Differentiable dynamical systems
ISBN : 9780821809297

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Analyzing Multiscale Phenomena Using Singular Perturbation Methods by Jane Cronin Pdf

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.

Author : J. Kevorkian,J.D. Cole
Publisher : Springer Science & Business Media
Page : 569 pages
File Size : 54,5 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475742138

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Perturbation Methods in Applied Mathematics by J. Kevorkian,J.D. Cole Pdf

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.

Author : James A. Murdock
Publisher : Wiley-Interscience
Page : 540 pages
File Size : 53,6 Mb
Release : 1991
Category : Mathematics
ISBN : UOM:39015019441081

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Perturbations by James A. Murdock Pdf

This is a course in perturbation theory for the solution of algebraic and differential equations, especially ordinary differential equations. It covers all of the methods commonly used in both regular and singular perturbations: Taylor series,

Author : Mark H. Holmes
Publisher : Springer Science & Business Media
Page : 344 pages
File Size : 49,9 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 : Christopher K.R.T. Jones,Alexander I. Khibnik
Publisher : Springer Science & Business Media
Page : 278 pages
File Size : 49,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461301172

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Multiple-Time-Scale Dynamical Systems by Christopher K.R.T. Jones,Alexander I. Khibnik Pdf

Systems with sub-processes evolving on many different time scales are ubiquitous in applications: chemical reactions, electro-optical and neuro-biological systems, to name just a few. This volume contains papers that expose the state of the art in mathematical techniques for analyzing such systems. Recently developed geometric ideas are highlighted in this work that includes a theory of relaxation-oscillation phenomena in higher dimensional phase spaces. Subtle exponentially small effects result from singular perturbations implicit in certain multiple time scale systems. Their role in the slow motion of fronts, bifurcations, and jumping between invariant tori are all explored here. Neurobiology has played a particularly stimulating role in the development of these techniques and one paper is directed specifically at applying geometric singular perturbation theory to reveal the synchrony in networks of neural oscillators.

Author : Jan Awrejcewicz,Roman Starosta,Grażyna Sypniewska-Kamińska
Publisher : CRC Press
Page : 411 pages
File Size : 42,6 Mb
Release : 2022-05-10
Category : Mathematics
ISBN : 9781000581256

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Asymptotic Multiple Scale Method in Time Domain by Jan Awrejcewicz,Roman Starosta,Grażyna Sypniewska-Kamińska Pdf

This book offers up novel research which uses analytical approaches to explore nonlinear features exhibited by various dynamic processes. Relevant to disciplines across engineering and physics, the asymptotic method combined with the multiple scale method is shown to be an efficient and intuitive way to approach mechanics. Beginning with new material on the development of cutting-edge asymptotic methods and multiple scale methods, the book introduces this method in time domain and provides examples of vibrations of systems. Clearly written throughout, it uses innovative graphics to exemplify complex concepts such as nonlinear stationary and nonstationary processes, various resonances and jump pull-in phenomena. It also demonstrates the simplification of problems through using mathematical modelling, by employing the use of limiting phase trajectories to quantify nonlinear phenomena. Particularly relevant to structural mechanics, in rods, cables, beams, plates and shells, as well as mechanical objects commonly found in everyday devices such as mobile phones and cameras, the book shows how each system is modelled, and how it behaves under various conditions. It will be of interest to engineers and professionals in mechanical engineering and structural engineering, alongside those interested in vibrations and dynamics. It will also be useful to those studying engineering maths and physics.

Author : Jane Cronin
Publisher : American Mathematical Society(RI)
Page : 201 pages
File Size : 55,9 Mb
Release : 2014-05-10
Category : MATHEMATICS
ISBN : 0821892711

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Analyzing Multiscale Phenomena Using Singular Perturbation Methods by Jane Cronin Pdf

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, USA. 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.

Author : Christian Kuehn
Publisher : Springer
Page : 814 pages
File Size : 43,5 Mb
Release : 2015-02-25
Category : Mathematics
ISBN : 9783319123165

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Multiple Time Scale Dynamics by Christian Kuehn Pdf

This book provides an introduction to dynamical systems with multiple time scales. The approach it takes is to provide an overview of key areas, particularly topics that are less available in the introductory form. The broad range of topics included makes it accessible for students and researchers new to the field to gain a quick and thorough overview. The first of its kind, this book merges a wide variety of different mathematical techniques into a more unified framework. The book is highly illustrated with many examples and exercises and an extensive bibliography. The target audience of this book are senior undergraduates, graduate students as well as researchers interested in using the multiple time scale dynamics theory in nonlinear science, either from a theoretical or a mathematical modeling perspective.

Author : Robert E. Jr. O'Malley
Publisher : Elsevier
Page : 214 pages
File Size : 45,7 Mb
Release : 2012-12-02
Category : Mathematics
ISBN : 9780323162272

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Introduction to Singular Perturbations by Robert E. Jr. O'Malley Pdf

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 : E. J. Hinch
Publisher : Cambridge University Press
Page : 178 pages
File Size : 46,5 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 : Bernold Fiedler,Konrad Groger,Jurgen Sprekels
Publisher : World Scientific
Page : 838 pages
File Size : 41,8 Mb
Release : 2000-09-05
Category : Mathematics
ISBN : 9789814522168

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Equadiff 99 (In 2 Volumes) - Proceedings Of The International Conference On Differential Equations by Bernold Fiedler,Konrad Groger,Jurgen Sprekels Pdf

This book is a compilation of high quality papers focussing on five major areas of active development in the wide field of differential equations: dynamical systems, infinite dimensions, global attractors and stability, computational aspects, and applications. It is a valuable reference for researchers in diverse disciplines, ranging from mathematics through physics, engineering, chemistry, nonlinear science to the life sciences.

Author : Bernold Fiedler,Konrad Gröger,J. Sprekels
Publisher : World Scientific
Page : 846 pages
File Size : 52,7 Mb
Release : 2000
Category : Differential equations
ISBN : 9810249888

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International Conference on Differential Equations, Berlin, Germany, 1-7 August, 1999 by Bernold Fiedler,Konrad Gröger,J. Sprekels Pdf

This book is a compilation of high quality papers focussing on five major areas of active development in the wide field of differential equations: dynamical systems, infinite dimensions, global attractors and stability, computational aspects, and applications. It is a valuable reference for researchers in diverse disciplines, ranging from mathematics through physics, engineering, chemistry, nonlinear science to the life sciences