Sensitivity analysis of linearly-implicit differential-algebraic systems by one-step extrapolation

In this work we present an approach for the sensitivity analysis of linearly-implicit differential-algebraic equation systems. Solutions for both states and sensitivities are obtained by applying an extrapolated linearly implicit Euler discretization scheme. This approach is compared to the widely used sensitivity extensions of multistep BDF methods by means of case studies. Especially, we point out the benefit of this method in the context of dynamic optimization using the sequential approach.