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Estévez Schwarz, Diana; Lamour, René

Diagnosis of singular points of properly stated DAEs using automatic differentiation. (English) Zbl 1335.65067

Numer. Algorithms 70, No. 4, 777-805 (2015).
The authors propagate a diagnosis tool to detect and analyze singular points of differential-algebraic equations (DAEs) up to tractability index 2. The diagnosis tool is based on Taylor expansions of DAEs. The condition number of the matrix of the linearized DAEs can be used to detect hidden singularities. A drawback in principle is the costly computation of the matrix sequence along the solution. Here the authors propagate an implementation where it suffices to compute two projectors and use information provided by automatic differentiation. Finally, some numerical examples are presented.
Reviewer: Johannes Schropp (Konstanz)

Cited in 6 Documents

MSC:

65L80 Numerical methods for differential-algebraic equations
34A09 Implicit ordinary differential equations, differential-algebraic equations

Keywords:

singular point; automatic differentiation; golden ratio; differential-algebraic equations; tractability index 2; condition number; numerical example

Software:

AlgoPy
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Full Text: DOI

References:

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