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Diagnosis of singular points of properly stated DAEs using automatic differentiation

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Abstract

The reliability of numerical results provided by conventional numerical integration methods for ODEs or DAEs depends on the properties of the problem. In particular, since the solution may not be unique at singular points, arbitrary solutions may be obtained. For DAEs, such singularities may occur, if the structure or the dimension of the spaces related to the DAE change. Moreover, even though a numerical singularity is not given in a strict mathematical sense, the numerical behavior may be analogous for sensitive problems. In this contribution, we aim at a characterization of this sensitivity, considering the condition number of a suitable matrix related to the DAE that is constructed using automatic differentiation. We show how this approach, which builds on the projector based analysis, can be applied to properly stated DAEs of index up to 2.

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Authors and Affiliations

  1. Humboldt University, Berlin, Germany

    René Lamour

  2. Beuth Hochschule für Technik, Berlin, Germany

    Diana Estévez Schwarz

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

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Estévez Schwarz, D., Lamour, R. Diagnosis of singular points of properly stated DAEs using automatic differentiation. Numer Algor 70, 777–805 (2015). https://doi.org/10.1007/s11075-015-9973-x

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  • DOI: https://doi.org/10.1007/s11075-015-9973-x

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