A new algorithm for the index determination in DAEs by Taylor series using Algorithmic Differentiation

Rene' Lamour , Dagmar Monett-Diaz

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 10-4,34

MSC 2000

65L80 Methods for differential-algebraic equations

65D25 Numerical differentiation

68W30 Symbolic computation and algebraic computation

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 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.