On consistent initial conditions for circuit's 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. The new method does not employ burdensome techniques such as the QR factorization or singular value decomposition which require the order of n³ operations, where n is the size of the system. Therefore, these techniques are prohibitive for large circuits. The numerical experiments suggest that the method works reliably even for index-3 DAEs. Furthermore, the method is not only restricted to initial value problems for DAEs but can also be applied to solvers for boundary value problems based on shooting techniques.