[2205.08105] Discretization of inherent ODEs and the geometric integration of DAEs with symmetries
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Mathematics > Numerical Analysis

arXiv:2205.08105 (math)
[Submitted on 17 May 2022]

Title:Discretization of inherent ODEs and the geometric integration of DAEs with symmetries

Authors:Peter Kunkel, Volker Mehrmann
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Abstract:Discretization methods for differential-algebraic equations (DAEs) are considered that are based on the integration of an associated inherent ordinary differential equation (ODE). This allows to make use of any discretization scheme suitable for the numerical integration of ODEs. For DAEs with symmetries it is shown that the inherent ODE can be constructed in such a way that it inherits the symmetry properties of the given DAE and geometric properties of its flow. This in particular allows the use of geometric integration schemes with a numerical flow that has analogous geometric properties.
Subjects: Numerical Analysis (math.NA); Optimization and Control (math.OC)
MSC classes: 37J06, 65L80, 65L05, 65P10
Cite as: arXiv:2205.08105 [math.NA]
  (or arXiv:2205.08105v1 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2205.08105

Submission history

From: Volker Mehrmann [view email]
[v1] Tue, 17 May 2022 06:01:20 UTC (16 KB)
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