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Rannacher, Rolf: Numerik 1: Numerik gewöhnlicher Differentialgleichungen, Heidelberg: Heidelberg University Publishing, 2017. DOI: 10.17885/heiup.258.342

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978-3-946054-31-3 (PDF)

978-3-946054-32-0 (Softcover)

Published 06/02/2017.

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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.

Contents
PDF
Titelei
Inhaltsverzeichnis
Literaturverzeichnis
Einleitung
Aus der Theorie der Anfangswertaufgaben
Einschrittmethoden
Numerische Stabilität
Lineare Mehrschrittmethoden
Extrapolationsmethode
Differentiell-algebraische Gleichungen (DAE)
Galerkin-Verfahren
Aus der Theorie der Randwertaufgaben
Schießverfahren
Differenzenverfahren
Variationsmethoden
Ausblick auf partielle Differentialgleichungen
Lösungen der Übungsaufgaben
Index