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A new projector based decoupling of linear DAEs for monitoring singularities

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Abstract

For higher index differential-algebraic equations (DAEs) some components of the solution depend on derivatives of the right-hand side. In this context, two main results are pointed out here. On the one hand, a description of the different types of undifferentiated components involved in the DAE is obtained by a projector-based decoupling. To this end, we define a new decoupling based on the number of inherent differentiations of the right-hand side that are required to determine each component. On the other hand, we introduce characteristic values that characterize the robustness of our numerically determined index-classification and decoupling as well as a meaningful indicator that permit the diagnosis of singular points.

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Authors and Affiliations

  1. Beuth Hochschule für Technik Berlin, Berlin, Germany

    Diana Estévez Schwarz

  2. Humboldt-University of Berlin, Berlin, Germany

    René Lamour

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

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Schwarz, D.E., Lamour, R. A new projector based decoupling of linear DAEs for monitoring singularities. Numer Algor 73, 535–565 (2016). https://doi.org/10.1007/s11075-016-0107-x

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  • DOI: https://doi.org/10.1007/s11075-016-0107-x

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