In this article we describe state-of-the-art approaches to calculate solutions and sensitivities for initial value problems (IVP) of semi-explicit systems of differential-algebraic equations of index one. We start with a description of the techniques we use to solve the systems efficiently with an adaptive BDF-method. Afterwards we focus on the computation of sensitivities using the principle of
Internal Numerical Differentiation
(IND) invented by Bock . We present a newly implemented reverse mode of IND to generate sensitivity information in an adjoint way. At the end we show a numerical comparison for the old and new approaches for sensitivity generation using the software package DAESOL-II , in which both approaches are implemented.
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