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Analysis and numerical solution of linear delay differential-algebraic equations

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Abstract

The analysis and numerical solution of initial value problems for linear delay differential-algebraic equations (DDAEs) is discussed. Characteristic properties of DDAEs are analyzed and the differences between causal and noncausal DDAEs are studied. The method of steps is analyzed and it is shown that it has to be modified for general DDAEs. The classification of ordinary delay differential equations is generalized to DDAEs, and a numerical solution procedure for general retarded and neutral DDAEs is constructed. The properties of the algorithm are studied and the theoretical results are illustrated with a numerical example.

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Acknowledgments

This work was supported by DFG Collaborative Research Centre 910, Control of self-organizing nonlinear systems: Theoretical methods and concepts of application. We thank Ma Vinh Tho for support in the numerical tests.

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Authors and Affiliations

  1. Institut für Mathematik, MA 4-5, TU Berlin, Straße des 17. Juni 136, 10623, Berlin, Germany

    Volker Mehrmann

  2. Department of Mathematics, Humboldt University of Berlin, 10099, Berlin, Germany

    Phi Ha

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  1. Phi Ha
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  2. Volker Mehrmann
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Correspondence to Volker Mehrmann.

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Communicated by Christian Lubich.

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Ha, P., Mehrmann, V. Analysis and numerical solution of linear delay differential-algebraic equations. Bit Numer Math 56, 633–657 (2016). https://doi.org/10.1007/s10543-015-0577-6

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  • DOI: https://doi.org/10.1007/s10543-015-0577-6

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