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Author | : Hans-Görg Roos |
Publisher | : Springer Science & Business Media |
Total Pages | : 364 |
Release | : 2013-06-29 |
Genre | : Mathematics |
ISBN | : 3662032066 |
Download Numerical Methods for Singularly Perturbed Differential Equations Book in PDF, ePub and Kindle
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.
Author | : Hans-Görg Roos |
Publisher | : Springer Science & Business Media |
Total Pages | : 599 |
Release | : 2008-09-17 |
Genre | : Mathematics |
ISBN | : 3540344675 |
Download Robust Numerical Methods for Singularly Perturbed Differential Equations Book in PDF, ePub and Kindle
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.
Author | : Hans-G. Roos |
Publisher | : Springer |
Total Pages | : 604 |
Release | : 2009-08-29 |
Genre | : Mathematics |
ISBN | : 9783540861973 |
Download Robust Numerical Methods for Singularly Perturbed Differential Equations Book in PDF, ePub and Kindle
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.
Author | : Hans-Görg Roos |
Publisher | : |
Total Pages | : 372 |
Release | : 2014-01-15 |
Genre | : |
ISBN | : 9783662032077 |
Download Numerical Methods for Singularly Perturbed Differential Equations Book in PDF, ePub and Kindle
Author | : John James Henry Miller |
Publisher | : World Scientific |
Total Pages | : 191 |
Release | : 2012 |
Genre | : Mathematics |
ISBN | : 9814390739 |
Download Fitted Numerical Methods for Singular Perturbation Problems Book in PDF, ePub and Kindle
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.
Author | : Lubin Vulkov |
Publisher | : Nova Publishers |
Total Pages | : 298 |
Release | : 2000 |
Genre | : Mathematics |
ISBN | : 9781560728481 |
Download Analytical and Numerical Methods for Convection-dominated and Singularly Perturbed Problems Book in PDF, ePub and Kindle
This volume is the Proceedings of the Workshop on Analytical and Computational Methods for Convection-Dominated and Singularly Perturbed Problems, which took place in Lozenetz, Bulgaria, 27-31 August 1998. The workshop attracted about 50 participants from 12 countries. The volume includes 13 invited lectures and 19 contributed papers presented at the workshop and thus gives an overview of the latest developments in both the theory and applications of advanced numerical methods to problems having boundary and interior layers. There was an emphasis on experiences from the numerical analysis of such problems and on theoretical developments. The aim of the workshop was to provide an opportunity for scientists from the East and the West, who develop robust methods for singularly perturbed and related problems and also who apply these methods to real-life problems, to discuss recent achievements in this area and to exchange ideas with a view of possible research co-operation.
Author | : Luminita Barbu |
Publisher | : Springer Science & Business Media |
Total Pages | : 231 |
Release | : 2007-12-14 |
Genre | : Mathematics |
ISBN | : 3764383313 |
Download Singularly Perturbed Boundary-Value Problems Book in PDF, ePub and Kindle
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.
Author | : Paul Farrell |
Publisher | : CRC Press |
Total Pages | : 298 |
Release | : 2000-03-30 |
Genre | : Science |
ISBN | : 9781584881926 |
Download Robust Computational Techniques for Boundary Layers Book in PDF, ePub and Kindle
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.
Author | : Paul Farrell |
Publisher | : CRC Press |
Total Pages | : 256 |
Release | : 2000-03-30 |
Genre | : Computers |
ISBN | : 148228572X |
Download Robust Computational Techniques for Boundary Layers Book in PDF, ePub and Kindle
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 pres
Author | : Grigory I. Shishkin |
Publisher | : CRC Press |
Total Pages | : 409 |
Release | : 2008-09-22 |
Genre | : Mathematics |
ISBN | : 0203492412 |
Download Difference Methods for Singular Perturbation Problems Book in PDF, ePub and Kindle
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