Robust Numerical Methods For Singularly Perturbed Differential Equations

Author : Hans-Görg Roos
Publisher : Springer Science & Business Media
ISBN 13 : 3540344675
Total Pages : 599 pages
Book Rating : 4.74/5 ( download)

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Download or read book Robust Numerical Methods for Singularly Perturbed Differential Equations written by Hans-Görg Roos and published by Springer Science & Business Media. This book was released on 2008-09-17 with total page 599 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Springer Science & Business Media
ISBN 13 : 3662032066
Total Pages : 364 pages
Book Rating : 4.60/5 ( download)

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Download or read book Numerical Methods for Singularly Perturbed Differential Equations written by Hans-Görg Roos and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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-G. Roos
Publisher : Springer
ISBN 13 : 9783540861973
Total Pages : 604 pages
Book Rating : 4.71/5 ( download)

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Download or read book Robust Numerical Methods for Singularly Perturbed Differential Equations written by Hans-G. Roos and published by Springer. This book was released on 2009-08-29 with total page 604 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 :
ISBN 13 : 9783662032077
Total Pages : 372 pages
Book Rating : 4.74/5 ( download)

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Download or read book Numerical Methods for Singularly Perturbed Differential Equations written by Hans-Görg Roos and published by . This book was released on 2014-01-15 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : John James Henry Miller
Publisher : World Scientific
ISBN 13 : 9814390739
Total Pages : 191 pages
Book Rating : 4.36/5 ( download)

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Download or read book Fitted Numerical Methods for Singular Perturbation Problems written by John James Henry Miller and published by World Scientific. This book was released on 2012 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Luminita Barbu
Publisher : Springer Science & Business Media
ISBN 13 : 3764383313
Total Pages : 231 pages
Book Rating : 4.12/5 ( download)

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Download or read book Singularly Perturbed Boundary-Value Problems written by Luminita Barbu and published by Springer Science & Business Media. This book was released on 2007-12-14 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
ISBN 13 : 148228572X
Total Pages : 256 pages
Book Rating : 4.27/5 ( download)

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Download or read book Robust Computational Techniques for Boundary Layers written by Paul Farrell and published by CRC Press. This book was released on 2000-03-30 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Valarmathi Sigamani
Publisher : Springer Nature
ISBN 13 : 9811675465
Total Pages : 218 pages
Book Rating : 4.61/5 ( download)

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Download or read book Differential Equations and Applications written by Valarmathi Sigamani and published by Springer Nature. This book was released on 2022-01-24 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects select papers presented at the International Conference on Applications of Basic Sciences, held at Tiruchirappalli, Tamil Nadu, India, from 19-21 November 2019. The book discusses topics on singular perturbation problems, differential equations, numerical analysis, fuzzy logics, fuzzy differential equations, and mathematical physics, and their interdisciplinary applications in all areas of basic sciences: mathematics, physics, chemistry, and biology. It will be useful to researchers and scientists in all disciplines of basic sciences. This book will be very useful to know the different scientific approaches for a single physical system.

Author : Grigory I. Shishkin
Publisher : CRC Press
ISBN 13 : 0203492412
Total Pages : 409 pages
Book Rating : 4.13/5 ( download)

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Download or read book Difference Methods for Singular Perturbation Problems written by Grigory I. Shishkin and published by CRC Press. This book was released on 2008-09-22 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Lubin Vulkov
Publisher : Nova Publishers
ISBN 13 : 9781560728481
Total Pages : 298 pages
Book Rating : 4.85/5 ( download)

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Download or read book Analytical and Numerical Methods for Convection-dominated and Singularly Perturbed Problems written by Lubin Vulkov and published by Nova Publishers. This book was released on 2000 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.