Monitoring Singularities While Integrating DAEs
Modern simulation tools for ODEs/DAEs allow a direct input of equations that are solved at the push of a button. However, if the mathematical assumptions that guarantee the correctness of the solution are not given, then no reliable results can be expected. Automatic (or algorithmic) differentiation (AD) opens new possibilities to analyze and solve ODEs/DAEs. In this paper, we outline how the index determination, the computation of consistent initial values, the integration and the diagnosis of singular points can be reliably carried out for DAEs up to index 3. The approach uses the projector based analysis for DAEs employing AD.
KeywordsDifferential-algebraic equations Taylor series Singularity Automatic differentiation
The authors are indebted to Roswitha März for many fruitful discussions.
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