Recent Progress in Extrapolation Methods for Ordinary Differential Equations

The paper is intended to give a survey on the state-of-the-art of extrapolation methods for initial value problems in ordinary differential equation systems. All basic discretizations, which are suited for combination with extrapolation, are discussed and evaluated. Both nonstiff and stiff integration is covered. Extensive numerical comparisions lead to rules of thumb, which may be an aid for the decision when to use extrapolation methods (as opposed to RK methods or multistep methods). The paper is understood to give a new platform, from which further work in this field might start. For this reason, several lines for possibly promising further research are indicated.