Symbolic Methods for Implicit Differential Algebraic Equation Systems

GABRIELA JERONIMO

Buenos Aires

Workshop; Geometria de Ecuaciones Diferenciales Complejas, II; 2010

We will describe new geometric and algebraic techniques developed for thesymbolic treatment of implicit dierential algebraic equation (DAE) systems.More precisely, we will focus on the notion of dierentiation index for quasi-regular DAE systems.The dierentiation index is an invariant related to the complexity of solving the DAE system by means of numerical methods: these methods perform well for systems with dierentiation index at most 3 but they can be very inefficient for higher index systems. We will present a symbolic index reduction procedure based on techniques from computational algebraic geometry.Given a quasi-regular DAE system, the proposed method produces a semi-explicit equivalente system of index 1.