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

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

2010-08-30

arxiv.org/abs/1008.5080v1

Mathematics

Classical Analysis and ODEs

Scientific paper

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.

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