A geometric index reduction method for implicit systems of differential algebraic equations

LISI D'ALFONSO; GABRIELA JERONIMO; FRANÇOIS OLLIVIER; ALEXANDRE SEDOGLAVIC; PABLO SOLERNÓ

JOURNAL OF SYMBOLIC COMPUTATION

ACADEMIC PRESS LTD-ELSEVIER SCIENCE LTD

Lugar: Amsterdam; Año: 2011 vol. 46 p. 1114 - 1138

0747-7171

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