|
Showing 1 - 4 of
4 matches in All Departments
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.
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.
Numerische Mathematik ist ein zentrales Gebiet der Mathematik, das
f r vielf ltige Anwendungen die Grundlage bildet und das alle
Studierenden der Mathematik, Ingenieurwissenschaften, Informatik
und Physik kennenlernen.
Das vorliegende Lehrbuch ist eine didaktisch exzellente, besonders
sorgf ltig ausgearbeitete Einf hrung f r Anf nger. Eines der Ziele
dieses Buches ist es, die mathematischen Grundlagen der numerischen
Methoden zu liefern, ihre grundlegenden theoretischen Eigenschaften
(Stabilit t, Genauigkeit, Komplexit t)zu analysieren, und ihre
Leistungsf higkeit an Beispielen und Gegenbeispielen mittels MATLAB
zu demonstrieren. Die besondere Sorgfalt, die den Anwendungen und
betreffenden Softwareentwicklungen gewidmet wurde, macht das
vorliegende Werk auch f r Studenten mit abgeschlossenem Studium,
Wissenschaftler und Anwender des wissenschaftlichen Rechnens in
vielen Berufsfeldern zu einem unverzichtbaren Arbeitsmittel. Inhalt
von Band 2 siehe ToC.
Die Finite-Elemente-Methode ist eine grundlegende mathematische
Technik zur Behandlung von Differentialgleichungs- und
Variationsproblemen, die
in Physik und Mechanik, im Bau- und Ingenieurwesen sowie in
Elektrotechnik und Mechatronik auftreten.
Das vorliegende Buch ist die vierte Auflage des bewahrten
Standardwerks der drei Autoren. Es ist speziell fur
Naturwissenschaftler und Ingenieure
geeignet, die die mathematischen Grundlagen der Methode
kennenlernen wollen. Das Lehrbuch wurde grundlich uberarbeitet,
zudem u.a. durch Hinweise auf unstetige Galerkin-Methoden und
verschiedene Varianten von a posteriori Fehlerabschatzungen sowie
Literatur- und Softwareverweise auf den aktuellen Stand
gebracht.
|
You may like...
Loot
Nadine Gordimer
Paperback
(2)
R398
R330
Discovery Miles 3 300
Loot
Nadine Gordimer
Paperback
(2)
R398
R330
Discovery Miles 3 300
|