The Theory Of Singular Perturbations
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The Theory Of Singular Perturbations
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Author : E.M. de Jager
language : en
Publisher: Elsevier
Release Date : 1996-11-08
The Theory Of Singular Perturbations written by E.M. de Jager and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-11-08 with Mathematics categories.
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 Perturbation Theory
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Author : Donald R. Smith
language : en
Publisher: Cambridge University Press
Release Date : 1985-08-30
Singular Perturbation Theory written by Donald R. Smith and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-08-30 with Mathematics categories.
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.
Singular Perturbation Theory
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Author : Lindsay A. Skinner
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-05-11
Singular Perturbation Theory written by Lindsay A. Skinner 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 2011-05-11 with Mathematics categories.
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.
Algebraic Analysis Of Singular Perturbation Theory
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Author : Takahiro Kawai
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
Algebraic Analysis Of Singular Perturbation Theory written by Takahiro Kawai 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 2005 with Mathematics categories.
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.
Introduction To The General Theory Of Singular Perturbations
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Author : S. A. Lomov
language : en
Publisher: American Mathematical Soc.
Release Date :
Introduction To The General Theory Of Singular Perturbations written by S. A. Lomov 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 with Mathematics categories.
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 Perturbation Theory
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Author : R.S. Johnson
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-12-28
Singular Perturbation Theory written by R.S. Johnson 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 2005-12-28 with Technology & Engineering categories.
The importance of mathematics in the study of problems arising from the real world, and the increasing success with which it has been used to model situations ranging from the purely deterministic to the stochastic, is well established. The purpose of the set of volumes to which the present one belongs is to make available authoritative, up to date, and self-contained accounts of some of the most important and useful of these analytical approaches and techniques. Each volume provides a detailed introduction to a specific subject area of current importance that is summarized below, and then goes beyond this by reviewing recent contributions, and so serving as a valuable reference source. The progress in applicable mathematics has been brought about by the extension and development of many important analytical approaches and techniques, in areas both old and new, frequently aided by the use of computers without which the solution of realistic problems would otherwise have been impossible.
Singular Perturbation Methods In Control
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Author : Petar Kokotovic
language : en
Publisher: SIAM
Release Date : 1999-01-01
Singular Perturbation Methods In Control written by Petar Kokotovic and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-01-01 with Mathematics categories.
This SIAM Classics edition of the 1986 book provides the theoretical foundation for representative control applications.
Analyzing Multiscale Phenomena Using Singular Perturbation Methods
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Author : Jane Cronin
language : en
Publisher: American Mathematical Soc.
Release Date :
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 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.
Fluid Mechanics And Singular Perturbations
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Author : Paco Lagerstrom
language : en
Publisher: Elsevier
Release Date : 2012-12-02
Fluid Mechanics And Singular Perturbations written by Paco Lagerstrom and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-02 with Science categories.
Fluid Mechanics and Singular Perturbations: A Collection of Papers by Saul Kaplun focuses on the works and contributions of Saul Kaplun to the studies of fluid mechanics and singular perturbations. The book first discusses the role of coordinate system in boundary-layer theory. Boundary-layer approximations as limits of exact solutions; comparison of different boundary-layer solutions; and comparison with exact solution and choice of optimal are discussed. The text also looks at asymptotic experiment of Navier-Stokes solution for small Reynolds numbers; basic concepts in the theory of singular perturbations and their applications to flow at small Reynolds numbers; and low Reynolds number flow. The book discusses as well a generalization of Poiseuille and Couette flows and nature of solutions of the boundary-layer equations. Numerical solutions and analyses are presented. The text also looks at compatibility condition for boundary layer equation at a point of zero skin friction. Intuitive background; the past-like solution and its principal asymptotic expansions; and class of compatible profiles are discussed. The book is a valuable source of information for readers who want to study fluid mechanics.
Singular Perturbations And Hysteresis
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Author : Michael P. Mortell
language : en
Publisher: SIAM
Release Date : 2005-01-01
Singular Perturbations And Hysteresis written by Michael P. Mortell and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-01-01 with Mathematics categories.
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.