ODEs or ordinary differential equations are used for modeling and quantifying time dependent processes. Chemical reactions, population growth, mechanical systems are examples for this. In this course, we give an introduction into the basic concepts underlying ODEs from a modeling point of view as well as from a mathematical point of view. We then consider numerical methods for the numerical solution of ODEsnd investigate properties such as approximation error and stability. This will include Runge-Kutta Methods and so called BDF methods. We will also shortly investigate modern approaches such as parallel-in-time integration. Numerical examples, programing, and mathematical analysis will be the tools for getting towards an understanding of dynamical systems and their properties.
- P. Deuflhard and F. Bornemann. Scientific computing with ordinary differential equations. Translated from the 1994 German original by Werner C. Rheinboldt. Texts in Applied Mathematics, 42. Springer-Verlag, New York, 2002.
- E. Hairer, S. P. Nørsett, and G. Wanner. Solving ordinary differential equations. I, vol- ume 8 of Springer Series in Computational Mathematics. Springer-Verlag, Berlin, second edition, 1993. Nonstiff problems.
- E. Hairer and G. Wanner. Solving ordinary differential equations. II, volume 14 of Springer Series in Computational Mathematics. Springer-Verlag, Berlin, second edition, 1996. Stiff and differential-algebraic problems.
- Arieh Iserles. A first course in the numerical analysis of differential equations. Cambridge Texts in Applied Mathematics. Cambridge University Press, Cambridge, second edition, 2009.