The Pantelides algorithm for delay differential-algebraic equations
Dynamical Systems
2020-10-30 v2 Numerical Analysis
Numerical Analysis
Abstract
We present a graph-theoretical approach that can detect which equations of a delay differential-algebraic equation (DDAE) need to be differentiated or shifted to construct a solution of the DDAE. Our approach exploits the observation that differentiation and shifting are very similar from a structural point of view, which allows us to generalize the Pantelides algorithm for differential-algebraic equations to the DDAE setting. The primary tool for the extension is the introduction of equivalence classes in the graph of the DDAE, which also allows us to derive a necessary and sufficient criterion for the termination of the new algorithm.
Cite
@article{arxiv.1908.01514,
title = {The Pantelides algorithm for delay differential-algebraic equations},
author = {Ines Ahrens and Benjamin Unger},
journal= {arXiv preprint arXiv:1908.01514},
year = {2020}
}