Singularly Perturbed Differential Equations

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Numerical Methods For Singularly Perturbed Differential Equations

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Author : Hans-Görg Roos
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29

Numerical Methods For Singularly Perturbed Differential Equations written by Hans-Görg Roos 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 2013-06-29 with Mathematics categories.

The analysis of singular perturbed differential equations began early in this century, when approximate solutions were constructed from asymptotic ex pansions. (Preliminary attempts appear in the nineteenth century [vD94].) This technique has flourished since the mid-1960s. Its principal ideas and methods are described in several textbooks. Nevertheless, asymptotic ex pansions may be impossible to construct or may fail to simplify the given problem; then numerical approximations are often the only option. The systematic study of numerical methods for singular perturbation problems started somewhat later - in the 1970s. While the research frontier has been steadily pushed back, the exposition of new developments in the analysis of numerical methods has been neglected. Perhaps the only example of a textbook that concentrates on this analysis is [DMS80], which collects various results for ordinary differential equations, but many methods and techniques that are relevant today (especially for partial differential equa tions) were developed after 1980.Thus contemporary researchers must comb the literature to acquaint themselves with earlier work. Our purposes in writing this introductory book are twofold. First, we aim to present a structured account of recent ideas in the numerical analysis of singularly perturbed differential equations. Second, this important area has many open problems and we hope that our book will stimulate further investigations.Our choice of topics is inevitably personal and reflects our own main interests.

Singularly Perturbed Differential Equations

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Author : Herbert Goering
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 1984-01-14

Singularly Perturbed Differential Equations written by Herbert Goering and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984-01-14 with Mathematics categories.

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Singularly Perturbed Differential Equations

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Author : Herbert Goering
language : en
Publisher:
Release Date : 1983

Singularly Perturbed Differential Equations written by Herbert Goering and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Boundary value problems categories.

Singularly Perturbed Boundary Value Problems

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Author : Luminita Barbu
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-14

Singularly Perturbed Boundary Value Problems written by Luminita Barbu 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 2007-12-14 with Mathematics categories.

This book offers a detailed asymptotic analysis of some important classes of singularly perturbed boundary value problems which are mathematical models for phenomena in biology, chemistry, and engineering. The authors are particularly interested in nonlinear problems, which have gone little-examined so far in literature dedicated to singular perturbations. The treatment presented here combines successful results from functional analysis, singular perturbation theory, partial differential equations, and evolution equations.

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 Methodology In Control Systems

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Author : Desineni S. Naidu
language : en
Publisher: IET
Release Date : 1988

Singular Perturbation Methodology In Control Systems written by Desineni S. Naidu and has been published by IET this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Technology & Engineering categories.

This book presents the twin topics of singular perturbation methods and time scale analysis to problems in systems and control. The heart of the book is the singularly perturbed optimal control systems, which are notorious for demanding excessive computational costs. The book addresses both continuous control systems (described by differential equations) and discrete control systems (characterised by difference equations).

Robust Numerical Methods For Singularly Perturbed Differential Equations

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Author : Hans-Görg Roos
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-09-17

Robust Numerical Methods For Singularly Perturbed Differential Equations written by Hans-Görg Roos 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 2008-09-17 with Mathematics categories.

This new edition incorporates new developments in numerical methods for singularly perturbed differential equations, focusing on linear convection-diffusion equations and on nonlinear flow problems that appear in computational fluid dynamics.

Fitted Numerical Methods For Singular Perturbation Problems Error Estimates In The Maximum Norm For Linear Problems In One And Two Dimensions Revised Edition

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Author : John J H Miller
language : en
Publisher: World Scientific
Release Date : 2012-02-29

Fitted Numerical Methods For Singular Perturbation Problems Error Estimates In The Maximum Norm For Linear Problems In One And Two Dimensions Revised Edition written by John J H Miller and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-02-29 with Mathematics categories.

Since the first edition of this book, the literature on fitted mesh methods for singularly perturbed problems has expanded significantly. Over the intervening years, fitted meshes have been shown to be effective for an extensive set of singularly perturbed partial differential equations. In the revised version of this book, the reader will find an introduction to the basic theory associated with fitted numerical methods for singularly perturbed differential equations. Fitted mesh methods focus on the appropriate distribution of the mesh points for singularly perturbed problems. The global errors in the numerical approximations are measured in the pointwise maximum norm. The fitted mesh algorithm is particularly simple to implement in practice, but the theory of why these numerical methods work is far from simple. This book can be used as an introductory text to the theory underpinning fitted mesh methods.

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.

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.