Sensitivity Generation in an Adaptive BDF-Method

Jan Albersmeyer () and Hans Georg Bock ()
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Jan Albersmeyer: University of Heidelberg, Interdisciplinary Center for Scientific Computing (IWR)
Hans Georg Bock: University of Heidelberg, Interdisciplinary Center for Scientific Computing (IWR)

A chapter in Modeling, Simulation and Optimization of Complex Processes, 2008, pp 15-24 from Springer

Abstract: 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.

Keywords: Directional Derivative; Initial Value Problem; Sensitivity Generation; Sensitivity Matrix; Iteration Matrix (search for similar items in EconPapers)
Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-79409-7_2

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DOI: 10.1007/978-3-540-79409-7_2

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