When integrating regular ODEs numerically, one tries carefully to match the dynamics of the numerical algorithm and the true solution behaviour well. Applying analogous numerical methods to DAEs, one expects to reach a similar harmonization. However, surprisingly, now the algorithms may behave very differently.
This talk aims at analysing the reason for that different behaviour. In particular, certain subspaces closely related to the geometry of the DAEs are shown to influence the dynamics of the algorithms significantly. Furthermore, with regard to matching the numerical and true dynamics better, regularization is revisited.