On consistent initial conditions for circuit DAEs with higher index

In this paper we study efficient numerical methods for obtaining consistent initial conditions for systems of differential-algebraic equations (DAEs) with higher index arising, for example, from electronic circuits. We show that the class of Gear´s backward differentiation formulas, unlike other multi-step techniques, are a useful means for obtaining consistent initial conditions when carefully implemented. Because the method employs sparse matrix techniques, it is efficient even for large circuits, The numerical experiments suggest that the method works reliably even for index-3 DAEs