Difference Methods For Singular Perturbation Problems
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Fitted Numerical Methods For Singular Perturbation Problems
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Author : John J. H. Miller
language : en
Publisher: World Scientific
Release Date : 2012
Fitted Numerical Methods For Singular Perturbation Problems 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 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.
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.
Robust Numerical Methods For Singularly Perturbed Differential Equations
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Author : Hans-G. Roos
language : en
Publisher: Springer
Release Date : 2010-11-18
Robust Numerical Methods For Singularly Perturbed Differential Equations written by Hans-G. Roos and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-18 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.
Difference Methods For Singular Perturbation Problems
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Author : Grigory I. Shishkin
language : en
Publisher: CRC Press
Release Date : 2008-09-22
Difference Methods For Singular Perturbation Problems written by Grigory I. Shishkin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-09-22 with Mathematics categories.
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 e
Difference Methods For Singular Perturbation Problems
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Author : Grigory I Shishkin
language : en
Publisher: CRC Press
Release Date : 2019-08-30
Difference Methods For Singular Perturbation Problems written by Grigory I Shishkin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-30 with categories.
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.
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.
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).
Fitted Numerical Methods For Singular Perturbation Problems
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Author : John James Henry Miller
language : en
Publisher: World Scientific
Release Date : 2012
Fitted Numerical Methods For Singular Perturbation Problems written by John James Henry 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 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.
Numerical Solution Of Boundary Value Problems For Ordinary Differential Equations
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Author : Uri M. Ascher
language : en
Publisher: SIAM
Release Date : 1988-01-01
Numerical Solution Of Boundary Value Problems For Ordinary Differential Equations written by Uri M. Ascher and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-01-01 with Mathematics categories.
This book is the most comprehensive, up-to-date account of the popular numerical methods for solving boundary value problems in ordinary differential equations. It aims at a thorough understanding of the field by giving an in-depth analysis of the numerical methods by using decoupling principles. Numerous exercises and real-world examples are used throughout to demonstrate the methods and the theory. Although first published in 1988, this republication remains the most comprehensive theoretical coverage of the subject matter, not available elsewhere in one volume. Many problems, arising in a wide variety of application areas, give rise to mathematical models which form boundary value problems for ordinary differential equations. These problems rarely have a closed form solution, and computer simulation is typically used to obtain their approximate solution. This book discusses methods to carry out such computer simulations in a robust, efficient, and reliable manner.
Chebyshev And Fourier Spectral Methods
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Author : John P. Boyd
language : en
Publisher: Courier Corporation
Release Date : 2001-12-03
Chebyshev And Fourier Spectral Methods written by John P. Boyd and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-12-03 with Mathematics categories.
Completely revised text focuses on use of spectral methods to solve boundary value, eigenvalue, and time-dependent problems, but also covers Hermite, Laguerre, rational Chebyshev, sinc, and spherical harmonic functions, as well as cardinal functions, linear eigenvalue problems, matrix-solving methods, coordinate transformations, methods for unbounded intervals, spherical and cylindrical geometry, and much more. 7 Appendices. Glossary. Bibliography. Index. Over 160 text figures.