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
Additionally, for technical aspects