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Methods And Applications Of Singular Perturbations


Methods And Applications Of Singular Perturbations
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Methods And Applications Of Singular Perturbations


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



Singular Perturbation Theory


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


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.


Singular perturbations and time-scale techniques were introduced to control engineering in the late 1960s and have since become common tools for the modeling, analysis, and design of control systems. In this SIAM Classics edition of the 1986 book, the original text is reprinted in its entirety (along with a new preface), providing once again the theoretical foundation for representative control applications. This book continues to be essential in many ways. It lays down the foundation of singular perturbation theory for linear and nonlinear systems, it presents the methodology in a pedagogical way that is not available anywhere else, and it illustrates the theory with many solved examples, including various physical examples and applications. So while new developments may go beyond the topics covered in this book, they are still based on the methodology described here, which continues to be their common starting point.



Singular Perturbation Methods For Ordinary Differential Equations


Singular Perturbation Methods For Ordinary Differential Equations
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Author : Robert E., Jr. O'Malley
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Singular Perturbation Methods For Ordinary Differential Equations written by Robert E., Jr. O'Malley 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 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.



Methods And Applications Of Singular Perturbations


Methods And Applications Of Singular Perturbations
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Author : Ferdinand Verhulst
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-06-28

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 2005-06-28 with Mathematics categories.


Contains well-chosen examples and exercises A student-friendly introduction that follows a workbook type approach



Algebraic Analysis Of Singular Perturbation Theory


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.



The Boundary Function Method For Singular Perturbed Problems


The Boundary Function Method For Singular Perturbed Problems
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Author : Adelaida B. Vasil'eva
language : en
Publisher: SIAM
Release Date : 1995-01-01

The Boundary Function Method For Singular Perturbed Problems written by Adelaida B. Vasil'eva and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-01-01 with Mathematics categories.


This book is devoted solely to the boundary function method, which is one of the asymptotic methods.



Singularly Perturbed Boundary Value Problems


Singularly Perturbed Boundary Value Problems
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Author : Matteo Dalla Riva
language : en
Publisher: Springer Nature
Release Date : 2021-10-01

Singularly Perturbed Boundary Value Problems written by Matteo Dalla Riva and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-01 with Mathematics categories.


This book is devoted to the analysis of the basic boundary value problems for the Laplace equation in singularly perturbed domains. The main purpose is to illustrate a method called Functional Analytic Approach, to describe the dependence of the solutions upon a singular perturbation parameter in terms of analytic functions. Here the focus is on domains with small holes and the perturbation parameter is the size of the holes. The book is the first introduction to the topic and covers the theoretical material and its applications to a series of problems that range from simple illustrative examples to more involved research results. The Functional Analytic Approach makes constant use of the integral representation method for the solutions of boundary value problems, of Potential Theory, of the Theory of Analytic Functions both in finite and infinite dimension, and of Nonlinear Functional Analysis. Designed to serve various purposes and readerships, the extensive introductory part spanning Chapters 1–7 can be used as a reference textbook for graduate courses on classical Potential Theory and its applications to boundary value problems. The early chapters also contain results that are rarely presented in the literature and may also, therefore, attract the interest of more expert readers. The exposition moves on to introduce the Functional Analytic Approach. A reader looking for a quick introduction to the method can find simple illustrative examples specifically designed for this purpose. More expert readers will find a comprehensive presentation of the Functional Analytic Approach, which allows a comparison between the approach of the book and the more classical expansion methods of Asymptotic Analysis and offers insights on the specific features of the approach and its applications to linear and nonlinear boundary value problems.



Perturbation Methods In Fluid Mechanics


Perturbation Methods In Fluid Mechanics
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Author : Milton Van Dyke
language : en
Publisher: Parabolic Press, Incorporated
Release Date : 1975

Perturbation Methods In Fluid Mechanics written by Milton Van Dyke and has been published by Parabolic Press, Incorporated this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with Science categories.