Main content

German original

Numerical Solution Methods for Differential Equations
(dt. Numerik von Differentialgleichungen)

Level, degree of commitment in original study programme Advanced module, compulsory elective module
Forms of teaching and learning,
workload
Lecture (4 SWS), recitation class (2 SWS),
270 hours (90 h attendance, 180 h private study)
Credit points,
formal requirements
9 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,
Jedes zweite Wintersemester
Person in charge of the module's outline Prof. Dr. Stephan Dahlke

Contents

Supplementary fundamentals to differential equations, methods for ordinary initial and boundary value problems, e.g. also for stiff problems. Standard method for partial differential equations.


Qualification Goals

The students shall

  • generally learn to assess numerical methods in terms of applicability and usefulness,
  • be introduced to the discretization of differential equations, including methods for estimating and controlling the unavoidable approximation errors,
  • to know the classification of different problem forms in differential equations and the appropriate selection of methods,
  • recognise how strongly theoretical analysis determines the framework conditions for numerical methods; in particular, the importance of functional analytical concepts for numerical problems should become clear,
  • practice mathematical working methods (development of mathematical intuition and its formal justification, training of abstract assets, proof techniques),
  • improve their oral communication skills in the exercises by practicing free speech in front of an audience and during discussi

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

  • Deuflhard, P., Bornemann, F.: Numerische Mathematik II, de Gruyter 2002;
  • Strehmel, K., Weiner, R.: Numerik gewöhnlicher Differentialgleichungen, Teubner, 1995;
  • Hanke-Bourgeois, M.: Grundlagen der Numerischen Mathematik und des Wissenschaftlichen Rechnens, Teubner, 2002.



Please note:

This page describes a module according to the latest valid module guide in Sommersemester 2021. 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.