On an index reduction method by deflation for differential-algebraic   equations
  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. 
Fabien Monfreda and Jean-Claude Yakoubsohn
math.CA