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.
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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.Review:
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)
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Buchbeschreibung Springer-Verlag Gmbh Sep 2008, 2008. Buch. Buchzustand: Neu. Neuware - The analysis of singular perturbed di erential equations began early in the twentieth century, when approximate solutions were constructed from asy- totic expansions. (Preliminary attempts appear in the nineteenth century see[vD94].)Thistechniquehas ourishedsincethemid-1960sanditsprincipal ideas and methods are described in several textbooks; nevertheless, asy- totic expansions may be impossible to construct or may fail to simplify the given problem and then numerical approximations are often the only option. Thesystematicstudyofnumericalmethodsforsingularperturbationpr- lems started somewhat later in the 1970s. From this time onwards the - search frontier has steadily expanded, but the exposition of new developments in the analysis of these numerical methods has not received its due attention. The rst textbook that concentrated on this analysis was [DMS80], which collected various results for ordinary di erential equations. But after 1980 no further textbook appeared until 1996, when three books were published: Miller et al. [MOS96], which specializes in upwind nite di erence methods on Shishkin meshes, Morton s book [Mor96], which is a general introduction to numerical methods for convection-di usion problems with an emphasis on the cell-vertex nite volume method, and [RST96], the rst edition of the present book. Nevertheless many methods and techniques that are important today, especially for partial di erential equations, were developed after 1996. 604 pp. Englisch. Artikel-Nr. 9783540344667