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

Abstract. We present an approach for determining the tractability index us-ing 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 sup-porting 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 ex-perimental results we have obtained with them