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

TL;DR

This paper introduces a geometric index reduction method for quasi-regular differential algebraic equations, transforming complex systems into simpler semi-explicit forms using a Kronecker-type algorithm with bounded complexity.

Contribution

It presents a novel geometric approach to reduce the index of quasi-regular DAE systems to a semi-explicit form via a bounded complexity Kronecker-type algorithm.

Findings

Any quasi-regular DAE system can be transformed into a semi-explicit form.

The method uses a Kronecker-type algorithm with bounded complexity.

The resulting system has a single algebraic equation and an under-determined ODE.

Abstract

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.