Difference Methods For Singular Perturbation Problems

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Difference Methods for Singular Perturbation Problems

Grigory I. Shishkin,Lidia P. Shishkina
Difference Methods for Singular Perturbation Problems Book PDF

Author : Grigory I. Shishkin,Lidia P. Shishkina
Publisher : CRC Press
Page : 408 pages
File Size : 49,7 Mb
Release : 2008-09-22
Category : Mathematics
ISBN : 0203492412

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Difference Methods for Singular Perturbation Problems by Grigory I. Shishkin,Lidia P. Shishkina Pdf

Difference Methods for Singular Perturbation Problems focuses on the development of robust difference schemes for wide classes of boundary value problems. It justifies the ε-uniform convergence of these schemes and surveys the latest approaches important for further progress in numerical methods. The first part of the book explores boundary value problems for elliptic and parabolic reaction-diffusion and convection-diffusion equations in n-dimensional domains with smooth and piecewise-smooth boundaries. The authors develop a technique for constructing and justifying ε uniformly convergent difference schemes for boundary value problems with fewer restrictions on the problem data. Containing information published mainly in the last four years, the second section focuses on problems with boundary layers and additional singularities generated by nonsmooth data, unboundedness of the domain, and the perturbation vector parameter. This part also studies both the solution and its derivatives with errors that are independent of the perturbation parameters. Co-authored by the creator of the Shishkin mesh, this book presents a systematic, detailed development of approaches to construct ε uniformly convergent finite difference schemes for broad classes of singularly perturbed boundary value problems.

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

Miller John J H,O'riordan Eugene,Shishkin G I
Fitted Numerical Methods For Singular Perturbation Problems Error Estimates In The Maximum Norm For Linear Problems In One And Two Dimensions Revised Edition Book PDF

Author : Miller John J H,O'riordan Eugene,Shishkin G I
Publisher : World Scientific
Page : 192 pages
File Size : 49,7 Mb
Release : 2012-02-29
Category : Mathematics
ISBN : 9789814452779

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Fitted Numerical Methods For Singular Perturbation Problems: Error Estimates In The Maximum Norm For Linear Problems In One And Two Dimensions (Revised Edition) by Miller John J H,O'riordan Eugene,Shishkin G I Pdf

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.

Robust Numerical Methods for Singularly Perturbed Differential Equations

Hans-Görg Roos,Martin Stynes,Lutz Tobiska
Robust Numerical Methods for Singularly Perturbed Differential Equations Book PDF

Author : Hans-Görg Roos,Martin Stynes,Lutz Tobiska
Publisher : Springer Science & Business Media
Page : 599 pages
File Size : 47,8 Mb
Release : 2008-09-17
Category : Mathematics
ISBN : 9783540344674

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Robust Numerical Methods for Singularly Perturbed Differential Equations by Hans-Görg Roos,Martin Stynes,Lutz Tobiska Pdf

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

John James Henry Miller,Eugene O'Riordan,G. I. Shishkin
Fitted Numerical Methods for Singular Perturbation Problems Book PDF

Author : John James Henry Miller,Eugene O'Riordan,G. I. Shishkin
Publisher : World Scientific
Page : 191 pages
File Size : 44,6 Mb
Release : 2012
Category : Mathematics
ISBN : 9789814390736

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Fitted Numerical Methods for Singular Perturbation Problems by John James Henry Miller,Eugene O'Riordan,G. I. Shishkin Pdf

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.

Multiple Scale and Singular Perturbation Methods

J.K. Kevorkian,J.D. Cole
Multiple Scale and Singular Perturbation Methods Book PDF

Author : J.K. Kevorkian,J.D. Cole
Publisher : Springer Science & Business Media
Page : 642 pages
File Size : 49,9 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.

Singular Perturbation Methodology in Control Systems

Desineni S. Naidu
Singular Perturbation Methodology in Control Systems Book PDF

Author : Desineni S. Naidu
Publisher : IET
Page : 314 pages
File Size : 42,5 Mb
Release : 1988
Category : Technology & Engineering
ISBN : 086341107X

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Singular Perturbation Methodology in Control Systems by Desineni S. Naidu Pdf

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).

Singular Perturbation Methods for Ordinary Differential Equations

Robert E., Jr. O'Malley
Singular Perturbation Methods for Ordinary Differential Equations Book PDF

Author : Robert E., Jr. O'Malley
Publisher : Springer Science & Business Media
Page : 234 pages
File Size : 46,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461209775

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Singular Perturbation Methods for Ordinary Differential Equations by Robert E., Jr. O'Malley Pdf

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.

Numerical Methods for Singularly Perturbed Differential Equations

Hans-Görg Roos,Martin Stynes,Lutz Tobiska
Numerical Methods for Singularly Perturbed Differential Equations Book PDF

Author : Hans-Görg Roos,Martin Stynes,Lutz Tobiska
Publisher : Springer Science & Business Media
Page : 364 pages
File Size : 40,7 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9783662032060

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Numerical Methods for Singularly Perturbed Differential Equations by Hans-Görg Roos,Martin Stynes,Lutz Tobiska Pdf

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.

Numerical Analysis of Singular Perturbation Problems

P. W. Hemker,John James Henry Miller
Numerical Analysis of Singular Perturbation Problems Book PDF

Author : P. W. Hemker,John James Henry Miller
Publisher : Unknown
Page : 520 pages
File Size : 54,5 Mb
Release : 1979
Category : Mathematics
ISBN : UOM:39015009241061

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Numerical Analysis of Singular Perturbation Problems by P. W. Hemker,John James Henry Miller Pdf

14 lectures by the invited speakers and 14 shorter contributions from the other speakers (pref.)

Fitted Numerical Methods for Singular Perturbation Problems

John J. H. Miller
Fitted Numerical Methods for Singular Perturbation Problems Book PDF

Author : John J. H. Miller
Publisher : World Scientific
Page : 191 pages
File Size : 51,7 Mb
Release : 2012
Category : Mathematics
ISBN : 9789814390743

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Fitted Numerical Methods for Singular Perturbation Problems by John J. H. Miller Pdf

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.

Introduction to Singular Perturbations

Robert E. Jr. O'Malley
Introduction to Singular Perturbations Book PDF

Author : Robert E. Jr. O'Malley
Publisher : Elsevier
Page : 214 pages
File Size : 47,7 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.

Singularly Perturbed Boundary-Value Problems

Luminita Barbu,Gheorghe Morosanu
Singularly Perturbed Boundary Value Problems Book PDF

Author : Luminita Barbu,Gheorghe Morosanu
Publisher : Springer Science & Business Media
Page : 231 pages
File Size : 41,8 Mb
Release : 2007-12-14
Category : Mathematics
ISBN : 9783764383312

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Singularly Perturbed Boundary-Value Problems by Luminita Barbu,Gheorghe Morosanu Pdf

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.

Singular Perturbation Theory

Lindsay A. Skinner
Singular Perturbation Theory Book PDF

Author : Lindsay A. Skinner
Publisher : Springer Science & Business Media
Page : 85 pages
File Size : 40,9 Mb
Release : 2011-05-11
Category : Mathematics
ISBN : 9781441999580

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Singular Perturbation Theory by Lindsay A. Skinner Pdf

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.

Singular Perturbation Methods for Ordinary Differential Equations

Robert E. O'Malley
Singular Perturbation Methods for Ordinary Differential Equations Book PDF

Author : Robert E. O'Malley
Publisher : Springer
Page : 248 pages
File Size : 42,5 Mb
Release : 1991-09-03
Category : Computers
ISBN : UOM:39076001186191

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Singular Perturbation Methods for Ordinary Differential Equations by Robert E. O'Malley Pdf

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

Donald R. Smith
Singular Perturbation Theory Book PDF

Author : Donald R. Smith
Publisher : Cambridge University Press
Page : 532 pages
File Size : 50,5 Mb
Release : 1985-08-30
Category : Mathematics
ISBN : 0521300428

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Singular-Perturbation Theory by Donald R. Smith Pdf

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.