The Common Ground of DAE Approaches
An overview of diverse DAE frameworks emphasizing their commonalities
DOI:
https://doi.org/10.52825/dae-p.v3i.2547Keywords:
Differential-Algebraic Equation, Higher Index, Regularity, Critical Points, Singularities, Structural Analysis, Persistent Structure, Index Concepts, Canonical Characteristic ValuesAbstract
We analyze different approaches to differential-algebraic equations with attention to the implemented rank conditions of various matrix functions. These conditions are apparently very different and certain rank drops in some matrix functions actually indicate a critical solution behavior. We look for common ground by considering various index and regularity notions from literature generalizing the Kronecker index of regular matrix pencils. In detail, starting from the most transparent reduction framework,
we work out a comprehensive regularity concept with canonical characteristic values applicable across all frameworks and prove the equivalence of thirteen distinct definitions of regularity.
This makes it possible to use the findings of all these concepts together.
Additionally, we show why not only the index but also these canonical characteristic values are crucial to describe the properties of the DAE.
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Copyright (c) 2025 Diana Estévez Schwarz, René Lamour, Roswitha März
This work is licensed under a Creative Commons Attribution 4.0 International License.
Accepted 2025-08-05
Published 2025-08-26