SciCADE 2013
International Conference on Scientific Computation and Differential Equations
September 16-20, 2013, Valladolid (Spain)

Invited Talk

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Diagnosis of Singular Points of DAEs

D. Estevez-Schwarz

Abstract
At a singular point of a DAE, the IVP fails to have a unique solution. All results concerning the existence and uniqueness of the IVP trace back to the Picard-Lindelöf-Theorem, whereas for DAEs the implicit function theorem is used. Proven results are given for so-called regularity-regions, that can be characterized considering linearized problems. Automatic (or Algorithmic) Differentiation (AD) opens new possibilities to realize an analysis of DAEs and to monitor the assumptions of regularity regions. We present how the index determination, the computation of consistent initial values, and the diagnosis of singular points can be reliably undertaken for DAEs up to index three. The approach uses the projector based analysis for DAEs employing AD. Different approaches are considered and illustrated by some examples, with particular emphasis on electrical circuits containing controlled sources.

Organized by         Universidad de Valladolid     IMUVA