Overview
- Includes supplementary material: sn.pub/extras
Part of the book series: Springer Series in Computational Mathematics (SSCM, volume 24)
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Table of contents (18 chapters)
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Front Matter
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Ordinary Differential Equations
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Front Matter
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Parabolic Initial-Boundary Value Problems in One Space Dimension
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Front Matter
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Elliptic and Parabolic Problems in Several Space Dimensions
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Front Matter
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The Incompressible Navier-Stokes Equations
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Front Matter
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Keywords
About this book
This considerably extended and completely revised second edition incorporates many new developments in the thriving field of numerical methods for singularly perturbed differential equations. It provides a thorough foundation for the numerical analysis and solution of these problems, which model many physical phenomena whose solutions exhibit layers. The book focuses on linear convection-diffusion equations and on nonlinear flow problems that appear in computational fluid dynamics. It offers a comprehensive overview of suitable numerical methods while emphasizing those with realistic error estimates. The book should be useful for scientists requiring effective numerical methods for singularly perturbed differential equations.
Reviews
From the reviews of the second edition:
"It is based on the classical technique of constructing asymptotic solutions to singular perturbation problems … . Singular perturbations occur in many important applications and developing asymptotic methods to study such problems continues to present challenges to the applied mathematician. … The authors are to be commended for … this important book, which describes a very fruitful and extensive interconnected international activity." (Robert E. O’Malley, SIAM Reviews, Vol. 51 (2), June, 2009)
"This book gives a survey of recent work on the numerical solution of singular-perturbation problems, mostly for convection-diffusion equations but also for reaction-diffusion equations. … One valuable feature of the book is the large number of remarks, which clarify details of the various methods. … The book is an essential reference for the researcher on computation of singular perturbation problems." (Gerald W. Hedstrom, Zentralblatt MATH, Vol. 1155, 2009)
"This book collects together some recent results in the area of numerical methods for singularly perturbed differential equations. … This well-written and lucid book will act as a useful state-of-the-art reference guide for researchers and students interested in understanding what has been published on robust numerical methods for singularly perturbed differential equations. In addition, it is clear from this book that many avenues of research remain open within the broad field of singularly perturbed problems." (Eugene O'Riordan, Mathematical Reviews, Issue 2009 f)
Authors and Affiliations
Bibliographic Information
Book Title: Robust Numerical Methods for Singularly Perturbed Differential Equations
Book Subtitle: Convection-Diffusion-Reaction and Flow Problems
Authors: Hans-Görg Roos, Martin Stynes, Lutz Tobiska
Series Title: Springer Series in Computational Mathematics
DOI: https://doi.org/10.1007/978-3-540-34467-4
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2008
Hardcover ISBN: 978-3-540-34466-7Published: 09 September 2008
Softcover ISBN: 978-3-642-07082-2Published: 18 November 2010
eBook ISBN: 978-3-540-34467-4Published: 17 September 2008
Series ISSN: 0179-3632
Series E-ISSN: 2198-3712
Edition Number: 2
Number of Pages: XIV, 604
Number of Illustrations: 41 b/w illustrations
Topics: Numerical Analysis, Mathematical and Computational Engineering, Analysis, Mathematical and Computational Biology, Statistics for Life Sciences, Medicine, Health Sciences, Theoretical and Computational Chemistry