A Geometric Index Reduction Method for Implicit Systems of Differential Algebraic Equations

A Geometric Index Reduction Method for Implicit Systems of Differential Algebraic Equations

This paper deals with the index reduction problem for the class of quasi-regular DAE systems. It is shown that any of these systems can be transformed to a generically equivalent first order DAE system consisting of a single purely algebraic (polynomial) equation plus an under-determined ODE (that i...

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Hauptverfasser: D'Alfonso, Lisi, Jeronimo, Gabriella, Ollivier, François, Sedoglavic, Alexandre, Solernó, Pablo
Format: Artikel
Sprache:eng
Schlagworte:
Computer Science - Symbolic Computation
Mathematics - Classical Analysis and ODEs
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Zusammenfassung:This paper deals with the index reduction problem for the class of quasi-regular DAE systems. It is shown that any of these systems can be transformed to a generically equivalent first order DAE system consisting of a single purely algebraic (polynomial) equation plus an under-determined ODE (that is, a semi-explicit DAE system of differentiation index 1) in as many variables as the order of the input system. This can be done by means of a Kronecker-type algorithm with bounded complexity.
DOI:10.48550/arxiv.1008.5080