This entry is from Winter semester 2022/23 and might be obsolete. You can find a current equivalent here.

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

 Level, degree of commitment Specialization module, depends on importing study program 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(s): 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 the degree program M.Sc. Mathematics. Subject, Origin Mathematics, M.Sc. Mathematics 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.

• 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.