Content:
Ordinary differential equations arise frequently in the modeling of physical, chemical, or biological phenomena.

The lecture deals with the numerical solution of ordinary differential equations and the estimation of the error between continuous and discrete solution.

1. Repetition
2. Differential-Algebraic Equations (DAEs)
3. Geometric Numerical Integration
4. Model Order Reduction
5. Multirate Integration
6. Dynamic Iteration
7. Shooting and Parallel-in-Time Methods
8. Exam Preparation

Target Audience:
The course is dedicated to students in mathematics, financial mathematics, IT and SII. Required course for master programme 'Computer Simulation in Science', first term in branch 'Mathematical Modelling'.

Remarks:

Prerequisite:
Knowledge of basic courses in mathematics (Analysis I-II, Linear Algebra I-II or similar) and Introduction to Numerical Mathematics (or: block course 'Introduction to Numerical Methods for Computer Simulation').

Lecture Notes:

Literature:

• E. Hairer, G. Wanner, S.P. Nørsett: Solving Ordinary Differential Equations I, Nonstiff Problems, Springer Series in Computational Mathematics, 1993.
• E. Hairer, G. Wanner: Solving Ordinary Differential Equations II, Stiff and Differential-Algebraic Problems, Springer Series in Computational Mathematics, 1996.
• K. Strehmel, R. Weiner, H. Podhaisky: Numerik gewöhnlicher Differentialgleichungen, Nichtsteife, steife und differential-algebraische Gleichungen, Vieweg+Teubner Verlag Wiesbaden, 2012.
• E. Hairer, G. Wanner, C. Lubich: Geometric Numerical Integration, Structure-Preserving Algorithms for Ordinary Differential Equations, (Springer Series in Computational Mathematics, 2006.
• J. Stoer, R. Bulirsch: Introduction to Numerical Analysis, Springer, Berlin 2002. (Chapter 7)
• J.  Stoer, R.  Bulirsch, Numerische Mathematik 2, Springer, Berlin 2005. (Kapitel 7)
• A.  Quarteroni, R.  Sacco, F.  Saleri, Numerical Mathematics, Springer, New York 2007. (Chapter 11)