On an index reduction method by deflation for differential-algebraic equations

TL;DR

This paper presents a deflation-based index reduction method for linear differential-algebraic equations, transforming them into simpler forms through substitution and differentiation, applicable to both constant and time-varying cases.

Contribution

It introduces a systematic deflation technique for reducing the index of linear DAEs, extending the approach to linear time-varying systems.

Findings

Method effectively reduces DAE index in classical examples.

Produces at most an ODE and algebraic constraints after reduction.

Extension to linear time-varying DAEs demonstrated.

Abstract

We study a deflation method to reduce and to solve linear dfferential-algebraic equations (DAEs). It consists to define a sequence of DAEs with index reduction of one unit by step. This is simultaneously performed by substitution and differentiation. At the end of process, we obtain at most an ODE and a list of algebraic constraints which solve the initial DAE. We show on classical examples how works the method. Moreover, we explain how this method extends in the case of linear time-varying DAEs.