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Discretization methods for differential-algebraic equations (DAEs) areconsidered that are based on the integration of an associated inherent ordinarydifferential equation (ODE). This allows to make use of any discretizationscheme suitable for the numerical integration of ODEs. For DAEs with symmetriesit is shown that the inherent ODE can be constructed in such a way that itinherits the symmetry properties of the given DAE and geometric properties ofits flow. This in particular allows the use of geometric integration schemeswith a numerical flow that has analogous geometric properties.

Discretization of inherent ODEs and the geometric integration of DAEs with symmetries