Numerical methods for ODEs

Ordinary differential equations (ODEs) often appear in the dynamical description of systems in physics, chemistry, biology, etc. It is only in particular cases that one can derive explicit solutions to ODEs: a numerical approximation is needed. The course covers numerical methods for ODEs such as Runge-Kutta methods and their linear stability analysis. Depending on the interest of the participants, more specialized topics will be covered. Examples of such specialized topics are: numerical methods for stiff problems, geometric numerical methods (i.e. structure-preserving numerical methods), Lie group integrators, or geometric mechanics. Exercises will illustrate and complement the theory presented during the lectures. Computer exercises illustrate the implementation and use of the presented numerical methods on small-scale problems.