We first show how to formulate DAEs geometrically using jet spaces and define the involutive form of a DAE. Then the solutions are defined as integral manifolds of a certain distribution related to the involutive form. As a byproduct we note that certain problems which are singular in classical framework become regular in this context.

We then show how to find the involutive form of a given DAE and discuss the concept of (differentiation) index: it measures the amount of symbolic computation needed to find the involutive form. We also discuss relations between our approach and other approaches presented in literature.

Then we numerically solve the DAE by Runge-Kutta type methods based on the involutive form. In particular, the drift-off is avoided. We argue by examples that the drift-off might destroy the qualitative behaviour. Finally we show how the jet space approach can be used to remove certain singularities in multibody systems.

MINISIMPOSIUM SESSION: 13. Numerical methods for DAEs