Advisor:

I want to take the opportunity to thank all the people that helped me during the preparation of this master this. First of all, my supervisor Dr. Alexander Ostermann who drew my interest to the topic of exponential integrators. Especially, I would like to mention his contribution to understanding and translating the proof of Leja regarding the maximal convergence of Leja points. I would also like to thank Stefan Rainer for proofreading this master thesis and offering suggestions for improvement. The hardware that allowed me to run quite extensive numerical simulations on multiple graphic processing units has been procured by the working group Numerical Analysis. Without this support it would have been difficult, at best, to test the algorithms given in this master thesis under "real world" conditions. In this regard, I would like to thank Wolfgang Kucher, who handled the setup and administration of before mentioned system. Last but not least I would also like to thank Martina Prugger for finding countless typos and other mistakes while proofreading this master thesis