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.

• 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.