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. ODE models in science
2. Short synopsis on theory of ODEs
3. One-step methods
4. Multi-step methods
5. Integration of stiff systems
6. Methods for differential algebraic equations
7. Two-point boundary value problems

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:

• R. Pulch, Numerical Analysis and Simulation of Ordinary Differential Equations, Lecture Notes, 2011.

Literature:

• 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)