Multiple Scale And Singular Perturbation Methods
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Multiple Scale And Singular Perturbation Methods
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Author : J. Kevorkian
language : en
Publisher:
Release Date : 1996-06-30
Multiple Scale And Singular Perturbation Methods written by J. Kevorkian and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-06-30 with categories.
Multiple Scale And Singular Perturbation Methods
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Author : J.K. Kevorkian
language : en
Publisher: Springer
Release Date : 2011-10-02
Multiple Scale And Singular Perturbation Methods written by J.K. Kevorkian and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-02 with Mathematics categories.
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.
Multiple Scale And Singular Perturbation Methods
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Author : J K Kevorkian
language : en
Publisher:
Release Date : 1996-05-15
Multiple Scale And Singular Perturbation Methods written by J K Kevorkian and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-05-15 with categories.
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.
Multiple Scale And Singular Perturbation Methods
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Author : J.K. Kevorkian
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Multiple Scale And Singular Perturbation Methods written by J.K. Kevorkian and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Methods And Applications Of Singular Perturbations
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Author : Ferdinand Verhulst
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-06-04
Methods And Applications Of Singular Perturbations written by Ferdinand Verhulst and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-06-04 with Mathematics categories.
Contains well-chosen examples and exercises A student-friendly introduction that follows a workbook type approach
Analyzing Multiscale Phenomena Using Singular Perturbation Methods
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Author : Jane Cronin
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
Analyzing Multiscale Phenomena Using Singular Perturbation Methods written by Jane Cronin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
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.
Geometric Singular Perturbation Theory Beyond The Standard Form
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Author : Martin Wechselberger
language : en
Publisher: Springer Nature
Release Date : 2020-02-21
Geometric Singular Perturbation Theory Beyond The Standard Form written by Martin Wechselberger and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-21 with Mathematics categories.
This volume provides a comprehensive review of multiple-scale dynamical systems. Mathematical models of such multiple-scale systems are considered singular perturbation problems, and this volume focuses on the geometric approach known as Geometric Singular Perturbation Theory (GSPT). It is the first of its kind that introduces the GSPT in a coordinate-independent manner. This is motivated by specific examples of biochemical reaction networks, electronic circuit and mechanic oscillator models and advection-reaction-diffusion models, all with an inherent non-uniform scale splitting, which identifies these examples as singular perturbation problems beyond the standard form. The contents cover a general framework for this GSPT beyond the standard form including canard theory, concrete applications, and instructive qualitative models. It contains many illustrations and key pointers to the existing literature. The target audience are senior undergraduates, graduate students and researchers interested in using the GSPT toolbox in nonlinear science, either from a theoretical or an application point of view. Martin Wechselberger is Professor at the School of Mathematics & Statistics, University of Sydney, Australia. He received the J.D. Crawford Prize in 2017 by the Society for Industrial and Applied Mathematics (SIAM) for achievements in the field of dynamical systems with multiple time-scales.
Introduction To Perturbation Methods
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Author : Mark H. Holmes
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-06-19
Introduction To Perturbation Methods written by Mark H. Holmes and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-06-19 with Mathematics categories.
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.
Asymptotic Multiple Scale Method In Time Domain
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Author : Jan Awrejcewicz
language : en
Publisher: CRC Press
Release Date : 2022-05-10
Asymptotic Multiple Scale Method In Time Domain written by Jan Awrejcewicz and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-10 with Mathematics categories.
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.
Multiple Time Scale Dynamics
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Author : Christian Kuehn
language : en
Publisher: Springer
Release Date : 2015-02-25
Multiple Time Scale Dynamics written by Christian Kuehn and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-02-25 with Mathematics categories.
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.