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Diagnosis of singular points of structured DAEs using automatic differentiation

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Abstract

At a singular point of a DAE, the IVP fails to have a unique solution. Hence, numerical integration methods cannot provide reasonable results. Unfortunately, common error control strategies do not always detect these circumstances and arbitrary solutions may be given to the user without warnings of any kind.

Automatic (or Algorithmic) Differentiation (AD) opens new possibilities to realize an analysis of DAEs and to monitor assumptions required for the existence and uniqueness of IVPs. We show how the diagnosis of singular points can be performed for structured quasi-linear DAEs up to index 2. Our approach uses the projector based analysis for DAEs employing AD. The resulting method is illustrated by several examples, with particular emphasis on simple electrical circuits containing controlled sources.

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Authors and Affiliations

  1. Beuth Hochschule für Technik Berlin, Berlin, Germany

    Diana Estévez Schwarz

  2. Humboldt-Universität zu Berlin, Berlin, Germany

    René Lamour

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  1. Diana Estévez Schwarz
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  2. René Lamour
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Correspondence to Diana Estévez Schwarz.

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Estévez Schwarz, D., Lamour, R. Diagnosis of singular points of structured DAEs using automatic differentiation. Numer Algor 69, 667–691 (2015). https://doi.org/10.1007/s11075-014-9919-8

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  • DOI: https://doi.org/10.1007/s11075-014-9919-8

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