Robust Numerical Methods for Singularly Perturbed Differential Equations : Convection-Diffusion and Flow Problems

Roos, Hans-Gorg; Stynes, Martin; Tobiska, Lutz

ISBN 10: 3540344667 / ISBN 13: 9783540344667

Editore: Springer, 2008

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• Titolo: Robust Numerical Methods for Singularly Perturbed Differential Equations : Convection-Diffusion and Flow Problems
• Editore: Springer
• Data di pubblicazione: 2008
• Lingua: Inglese
• ISBN 10: 3540344667
• ISBN 13: 9783540344667
• Rilegatura: Rilegato
• Edizione: seconda edizione
• Condizione: As New

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Riassunto

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, Mortons 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.

Dalla quarta di copertina

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.