2011-09-27Buch DOI: 10.18452/2821
A new algorithm for the index determination in DAEs by Taylor series using Algorithmic Differentiation
Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, Institut für Mathematik
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 realize the time differentiations using Algorithmic Differentiation techniques, specially by 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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