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A new algorithm for index determination in DAEs using algorithmic differentiation

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Abstract

We present an approach for determining the tractability index using truncated polynomial arithmetic. In particular, computing the index this way generates a sequence of matrices that contains itself derivatives. We implement the time differentiations using algorithmic differentiation techniques, specially using the standard ADOL-C package, with which calculating the derivatives becomes a simple shift and scaling of coefficients. We present the theory supporting the procedure we propose, as well as the implementation issues behind it to provide a convenient interface to the standard ADOL-C functionality. We give also examples of academic and practical problems and report several experimental results we have obtained with them.

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Authors and Affiliations

  1. Department of Mathematics, Humboldt-University of Berlin, Unter den Linden 6, 10099, Berlin, Germany

    René Lamour

  2. Computer Science Department and Department of Cooperative Studies, Berlin School of Economics and Law, Alt-Friedrichsfelde 60, 10315, Berlin, Germany

    Dagmar Monett

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  1. René Lamour
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  2. Dagmar Monett
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Correspondence to René Lamour.

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Lamour, R., Monett, D. A new algorithm for index determination in DAEs using algorithmic differentiation. Numer Algor 58, 261–292 (2011). https://doi.org/10.1007/s11075-011-9455-8

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