Abstract
The quality of numerical simulations of DAE models depends on basic assumptions that exclude singularities. In practice, most algorithms used in simulation tools do not check the assumed properties of the DAE. Consequently, 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. We aim at a characterization of this sensitivity, considering the condition number of a suitable matrix related to the DAE. Illustrative examples are given.
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Lamour, R., Estévez Schwarz, D. (2017). Discovering Singular Points in DAE Models. In: Bock, H., Phu, H., Rannacher, R., Schlöder, J. (eds) Modeling, Simulation and Optimization of Complex Processes HPSC 2015 . Springer, Cham. https://doi.org/10.1007/978-3-319-67168-0_8
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DOI: https://doi.org/10.1007/978-3-319-67168-0_8
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