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Monitoring Singularities While Integrating DAEs

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Progress in Differential-Algebraic Equations

Part of the book series: Differential-Algebraic Equations Forum ((DAEF))

Abstract

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.

Mathematics Subject Classification (2010) 65L80 ⋅ 65L05 ⋅ 41A58

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Acknowledgements

The authors are indebted to Roswitha März for many fruitful discussions.

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Authors and Affiliations

  1. B. Hochschule für Technik Berlin, Luxemburger Str. 10, 13353, Berlin, Germany

    Diana Estévez Schwarz

  2. Institut für Mathematik, Humboldt Universität zu Berlin, 10099, Berlin, Germany

    René Lamour

Authors
  1. Diana Estévez Schwarz
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  2. René Lamour
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Corresponding author

Correspondence to René Lamour .

Editor information

Editors and Affiliations

  1. Technische Universität Darmstadt, Graduate School CE, Darmstadt, Germany

    Sebastian Schöps

  2. Bergische Universität Wuppertal, Applied Math. and Numerical Analysis, Wuppertal, Germany

    Andreas Bartel

  3. Bergische Univeirsität Wuppertal, Applied Math. and Numerical Analysis, Wuppertal, Germany

    Michael Günther

  4. Eindhoven University of Technology, Dept. Mathematics & Comp. Sci., Eindhoven, The Netherlands

    E. Jan W. ter Maten

  5. Bergische Universität Wuppertal, Dept. Safety Control Engineering, Wuppertal, Germany

    Peter C Müller

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Schwarz, D.E., Lamour, R. (2014). Monitoring Singularities While Integrating DAEs. In: Schöps, S., Bartel, A., Günther, M., ter Maten, E., Müller, P. (eds) Progress in Differential-Algebraic Equations. Differential-Algebraic Equations Forum. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44926-4_4

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