Vienna contributions to the development of RK-methods Original Research Article

In 1965, H.J. Stetter moved from his home in Munich to Vienna, to take a newly created chair for Numerical Mathematics at the Technical University of Vienna. At the Technical University of Munich, since 1953, he had grown up in one of the first major research groups in the new area of Numerical Analysis, with one of the first electronic computers available since 1955. His own interests had been strongly tied to the computational solution of initial value problems in both ordinary and partial differential equations. He took these interests with him to Vienna where they spread to his students and collaborators. Thus, a research group in ODEs originated at the Technical University in Vienna and RK-methods were an important objective. In the following, we sketch the related activities and achievements of this group from 1965 to these days. The main emphasis has been given to the work related with stiff systems. In particular, Section 5 is devoted to a rather detailed discussion of the nature of stiffness and its implications on the convergence theory of RK-methods for nonlinear stiff problems from a point of view which has originated from the Vienna group since the late seventies.