Robust Numerical Methods For 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.
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.
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.
Robust Numerical Methods For Singularly Perturbed Differential Equations
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Author : Hans-G. Roos
language : en
Publisher: Springer
Release Date : 2009-08-29
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 2009-08-29 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.
Numerical Methods For Singularly Perturbed Differential Equations
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Author : Hans-Görg Roos
language : en
Publisher:
Release Date : 2014-01-15
Numerical Methods For Singularly Perturbed Differential Equations written by Hans-Görg Roos and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
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.
Numerical Methods For Elliptic And Parabolic Partial Differential Equations
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Author : Peter Knabner
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-06-26
Numerical Methods For Elliptic And Parabolic Partial Differential Equations written by Peter Knabner 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 2003-06-26 with Mathematics categories.
This text provides an application oriented introduction to the numerical methods for partial differential equations. It covers finite difference, finite element, and finite volume methods, interweaving theory and applications throughout. The book examines modern topics such as adaptive methods, multilevel methods, and methods for convection-dominated problems and includes detailed illustrations and extensive exercises.
Robust Computational Techniques For Boundary Layers
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Author : Paul Farrell
language : en
Publisher: CRC Press
Release Date : 2000-03-30
Robust Computational Techniques For Boundary Layers written by Paul Farrell and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-03-30 with Science categories.
Current standard numerical methods are of little use in solving mathematical problems involving boundary layers. In Robust Computational Techniques for Boundary Layers, the authors construct numerical methods for solving problems involving differential equations that have non-smooth solutions with singularities related to boundary layers. They present a new numerical technique that provides precise results in the boundary layer regions for the problems discussed in the book. They show that this technique can be adapted in a natural way to a real flow problem, and that it can be used to construct benchmark solutions for comparison with solutions found using other numerical techniques. Focusing on robustness, simplicity, and wide applicability rather than on optimality, Robust Computational Techniques for Boundary Layers provides readers with an understanding of the underlying principles and the essential components needed for the construction of numerical methods for boundary layer problems. It explains the fundamental ideas through physical insight, model problems, and computational experiments and gives details of the linear solvers used in the computations so that readers can implement the methods and reproduce the numerical results.
Analytic Methods For Partial Differential Equations
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Author : G. Evans
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Analytic Methods For Partial Differential Equations written by G. Evans 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.
The subject of partial differential equations holds an exciting and special position in mathematics. Partial differential equations were not consciously created as a subject but emerged in the 18th century as ordinary differential equations failed to describe the physical principles being studied. The subject was originally developed by the major names of mathematics, in particular, Leonard Euler and Joseph-Louis Lagrange who studied waves on strings; Daniel Bernoulli and Euler who considered potential theory, with later developments by Adrien-Marie Legendre and Pierre-Simon Laplace; and Joseph Fourier's famous work on series expansions for the heat equation. Many of the greatest advances in modern science have been based on discovering the underlying partial differential equation for the process in question. J ames Clerk Maxwell, for example, put electricity and magnetism into a unified theory by estab lishing Maxwell's equations for electromagnetic theory, which gave solutions for problems in radio wave propagation, the diffraction of light and X-ray developments. Schrodinger's equation for quantum mechankal processes at the atomic level leads to experimentally verifiable results which have changed the face of atomic physics and chemistry in the 20th century. In fluid mechanics, the Navier-Stokes' equations form a basis for huge number-crunching activities associated with such widely disparate topics as weather forcasting and the design of supersonic aircraft. Inevitably the study of partial differential equations is a large undertaking, and falls into several areas of mathematics.
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.