Numerics of Differential Equations

non-stiff and stiff integration of initial value problems, introduction to boundary value problems and optimal control; introduction to the numerical solution of partial differential equations (finite differences, finite elements, spectral methods) with a focus on problems in one spatial dimension, 2D for elliptic boundary value problems

After successful completion of this module the students are able to understand, to judge and to apply basic algorithms for the numerical solution of ordinary and partial differential equations. Students know and can apply the basic techniques for the assessment of discretization errors. They have learnt to think algorithmically and to realise complex algorithms on the computer.

MA0001 Analysis 1, MA0002 Analysis 2, MA0004 Linear Algebra 1, MA0005 Linear Algebra 2 and Discrete Structures, MA0008 Numerical Analysis

lecture, exercise module, assignments and programming for self-study
The module is offered as lectures with accompanying practice sessions. In the lectures, the contents will be presented in a talk with demonstrative examples, as well as through discussion with the students. The lectures should motivate the students to carry out their own analysis of the themes presented and to independently study the relevant literature. Corresponding to each lecture, practice sessions will be offered, in which exercise sheets and solutions will be available. In this way, students can deepen their understanding of the methods and concepts taught in the lectures and independently check their progress.

blackboard, computer experiments

- Deuflhard, Bornemann: Numerische Mathematik 2, 3. Auflage, de Gruyter 2008.
- Quarteroni, Sacco, Saleri: Numerische Mathematik 2, Springer 2002.
- Iserles, A.: A first course in the numerical analysis of differential equations. Cambridge University Press, Cambridge, 1996.

The module examination is based on a written exam (90 minutes). In the exam it will be assessed to which extent the students have understood the algorithmic numerical way of thinking by means of basic algorithms. Students have to show in a limited amount of time that they know and can apply basic techniques for the evaluation of the efficiency and accuracy of numerical algorithms and the estimation of approximation errors.