How to Cite

Rannacher, Rolf: Numerik 1: Numerik gewöhnlicher Differentialgleichungen, Heidelberg: Heidelberg University Publishing, 2017 (Lecture Notes). https://doi.org/10.17885/heiup.258.342

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Identifiers

https://doi.org/10.17885/heiup.258.342
ISBN 978-3-946054-31-3 (PDF)
ISBN 978-3-946054-32-0 (Softcover)

Published

06/02/2017

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Authors

Rolf Rannacher

Numerik 1

Numerik gewöhnlicher Differentialgleichungen

Lecture Notes

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 second part treats numerical methods for solving ordinary differential equations. Again theoretical as well as practical aspects are considered. The last chapter provides an outlook on numerical methods for partial differential equations. The  understanding of the contents requires besides the material of the first volume in this series “Numerik 0” only that prior knowledge as is usually provided in the basic Analysis and Linear Algebra courses. For facilitating self-learning the book contains theoretical and practical exercises with solutions.

Rolf Rannacher, 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.

Chapters

Table of Contents
Pages
PDF
Titelei
Inhaltsverzeichnis
v–viii
Literaturverzeichnis
ix
Einleitung
1–11
Aus der Theorie der Anfangswertaufgaben
13–41
Einschrittmethoden
43–71
Numerische Stabilität
73–98
Lineare Mehrschrittmethoden
99–126
Extrapolationsmethode
127–139
Differentiell-algebraische Gleichungen (DAE)
141–149
Galerkin-Verfahren
151–190
Aus der Theorie der Randwertaufgaben
191–197
Schießverfahren
199–212
Differenzenverfahren
213–231
Variationsmethoden
233–249
Ausblick auf partielle Differentialgleichungen
251–269
Lösungen der Übungsaufgaben
271–340
Index
341–344

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