A new algorithm for index determination in DAEs using algorithmic differentiation

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.

Pointwise numerical index determination of unstructured DAEs

“…). This was done for the differentiation index by (Campbell, Hollenbeck 1996, [4]), for the structural index by (Nedialkov, Pryce 2005-07, [13], [14], [15]) and for the tractability index by (Lamour, Monett Diaz 2011, [12]) with arbitrary projectors, but not widely orthogonal ones.…”