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 e.g. from electronic circuits. We show that the class of Gear's backward differentiation formulas, unlike other multi-step techniques, are 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.