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Rannacher, Rolf: Numerik 2: Numerik partieller Differentialgleichungen, Heidelberg: Heidelberg University Publishing, 2017. DOI: 10.17885/heiup.281.370

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978-3-946054-37-5 (PDF)

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Published 08/08/2017.


Rolf Rannacher

Numerik 2

Numerik partieller Differentialgleichungen

This introductory text is based on courses within a multi-semester cycle on “Numerical Mathematics” given by the author at Heidelberg University over a period of 25 years. The present third part is devoted to numerical methods for solving partial differential equations. Again theoretical as well as practical aspects are considered.

The understanding of the contents requires besides the material of the first two parts of this series, "Numerik 0 (Einführung in die Numerische Mathematik)" and "Numerik 1 - (Numerik gewöhnlicher  Differentialgleichungen)", only that prior knowledge as is usually provided in the basic Analysis and Linear Algebra courses. For facilitating self-learning the book contains theoretical exercises with solutions.

Retired Professor of Numerical Mathematics at Heidelberg University – study of Mathematics at the University of Frankfurt/Main, doctorate 1974, postdoctorate 1978 at Bonn University – 1979/1980 Vis. Assoc. Professor at the University of Michigan (Ann Arbor, USA), thereafter Professor at Erlangen and Saarbrücken, in Heidelberg since 1988 -- field of interest "Numerics of Partial Differential Equations", especially the "Finite Element Method" and its applications in the Natural Sciences and Engeneering; more than 160 scientific publications.

Kapitel 0: Einleitung
Kapitel 1: Theorie partieller Differentialgleichungen
Kapitel 2: Differenzen-Verfahren für elliptische Probleme
Kapitel 3: Finite-Elemente-Verfahren für elliptische Probleme
Kapitel 4: Lösung der FE-Gleichungen
Kapitel 5: Verfahren für parabolische Probleme
Kapitel 6: Verfahren für hyperbolische Probleme
Kapitel A: Lösungen der Übungsaufgaben