Implicit-Explicit Runge-Kutta time integration methods

The timetable of the course is as follow:

Friday 8 of November:
16:30 -- 19:30 Room G (instead of Data Fitting)
 
Monday 11 of November
09:00 -- 10:30 Room T.04
10:30 -- 12:30 Room C (instead of Data Fitting)
 
Tuesday 12 of November
08:30 -- 10:30 Room (T04) (instead of Mathematical modelling)
 
Wednesday 13 of November
10:30 -- 12:30 Room G (instead of Data Fitting)

The abstract of the minicourse is:

An important numerical strategy which is an integral part of many modern numerical schemes is the application of implicit-explicit (IMEX) or semi-implicit time integration methods. However, in the teaching curriculum these methods are not often taught. Therefore, this 12h course is dedicated to an introduction into IMEX Runge-Kutta methods which are additive Runge-Kutta schemes. The course will also entail a short repetition of explicit and implicit Runge-Kutta methods which are widely used in numerical schemes for the approximation of partial differential equations along the method of lines. 

The course focuses on the derivation of IMEX Runge-Kutta methods, in a theoretical as well as practical framework. Stability properties will be discussed as well as an outlook to stiff problems will be given. Due to the need to solve potentially non-linear implicit systems, linearization techniques, such as semi-linear IMEX Runge-Kutta will be addressed.

The course is targeted to doctoral students and interested Master students. The prerequisites consist of basic knowledge of ordinary differential equations (ODEs) and numerical methods for ODEs. Knowledge of hyperbolic partial differential equations is advantageous, as well as basic knowledge in numerical methods for linear and non-linear problems.