Introduction to Ordinary Differential Equations
Ordinary Differential Equations (ODEs) are the main mathematical tool for modeling and quantifying time dependent processes. Chemical reactions, population growth, mechanical systems are examples for this. Newton's second law is in fact an ODE. 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 ODEs and 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, programming, and mathematical analysis will be the tools for getting towards an understanding of dynamical systems and their properties.
RECOMMENDED COURSESIntroduction to Partial Differential Equations, Multiscale Methods, Numerical Algorithms, Software Atelier: Partial Differential Equations
- Iserles, Arieh. A first course in the numerical analysis of differential equations. No. 44. Cambridge university press, 2009.
- Boyce, William E. Differential equations: an introduction to modern methods and applications. John Wiley & Sons, 2010.
Additionally, for technical aspects
- Deuflhard, Peter, and Folkmar Bornemann. Scientific computing with ordinary differential equations. Vol. 42. Springer Science & Business Media, 2012.
- E. Hairer, S. P. Nørsett, and G. Wanner. Solving ordinary differential equations. I, volume 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.