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German original

Special Methods for Initial Value Problems
(dt. Spezialverfahren für Anfangswertprobleme)

Level, degree of commitment in original study programme Advanced module, compulsory elective module
Forms of teaching and learning,
workload
Lecture (3 SWS), recitation class (1 SWS),
180 hours (60 h attendance, 120 h private study)
Credit points,
formal requirements
6 CP
Course requirement: Successful completion of at least 50 percent of the points from the weekly exercises.
Examination type: Written or oral examination
Language,
Grading
German,
The grading is done with 0 to 15 points according to the examination regulations for study course M.Sc. Mathematics.
Original study programme M.Sc. Mathematik / Vertiefungsbereich Mathematik
Duration,
frequency
One semester,
Regelmäßig im Wechsel mit anderen advanced moduleen
Person in charge of the module's outline Prof. Dr. Stephan Dahlke

Contents

Procedures and terms for initial value problems with special problem requirements, such as large, stiff problems, problems with conservation laws. Parallel procedures


Qualification Goals

The students shall

  • recognize the limits of the usual standard procedures when special requirements from problems or computer architecture come to the fore,
  • to get to know the theoretical background and practical solution approaches for this requirement in order to be able to make a problem-adequate choice of methods in concrete cases,
  • to illustrate here how developments in natural sciences and computer science influence applied mathematics,
  • practice mathematical working methods (development of mathematical intuition and its formal justification, training of the ability to abstract, proof techniques),
  • improve their oral communication skills in the exercises by practicing free speech in front of an audience and during discussion.

Prerequisites

None. The competences taught in the following modules are recommended: either Foundations of Mathematics and Linear Algebra I and Linear Algebra II or Basic Linear Algebra, either Analysis I and Analysis II or Basic Real Analysis, Numerical Analysis.


Recommended Reading

  • Strehmel, K., Weiner, R.: Numerik gewöhnlicher Differentialgleichungen, Teubner, 1995;
  • Burrage, K: Parallel and sequential methods for ordinary differential equations, Clarendon Press;
  • Hairer, E., Luchich, C., Wanner, G.: Geometric numerical integration – Structure-preserving algorithms for ordinary differential equations, Springer.



Please note:

This page describes a module according to the latest valid module guide in Wintersemester 2020/21. Most rules valid for a module are not covered by the examination regulations and can therefore be updated on a semesterly basis. The following versions are available in the online module guide:

The module guide contains all modules, independent of the current event offer. Please compare the current course catalogue in Marvin.

The information in this online module guide was created automatically. Legally binding is only the information in the examination regulations (Prüfungsordnung). If you notice any discrepancies or errors, we would be grateful for any advice.