Abstract
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 [4]. 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 [1], in which both approaches are implemented.
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Albersmeyer, J., Bock, H.G. (2008). Sensitivity Generation in an Adaptive BDF-Method. In: Bock, H.G., Kostina, E., Phu, H.X., Rannacher, R. (eds) Modeling, Simulation and Optimization of Complex Processes. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79409-7_2
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DOI: https://doi.org/10.1007/978-3-540-79409-7_2
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