| Robust Numerical Methods for Singularly Perturbed Differential Equations: Convection-Diffusion-Reaction and Flow Problems Contributor(s): Roos, Hans-Görg (Author), Stynes, Martin (Author), Tobiska, Lutz (Author) |
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ISBN: 3642070825 ISBN-13: 9783642070822 Publisher: Springer OUR PRICE: $170.99 Product Type: Paperback - Other Formats Published: November 2010 |
| Additional Information |
| BISAC Categories: - Mathematics | Number Systems - Medical | Biostatistics - Mathematics | Applied |
| Dewey: 518.63 |
| Series: Springer Computational Mathematics |
| Physical Information: 1.25" H x 6.14" W x 9.21" (1.89 lbs) 604 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |