Consistent initialization for nonlinear index-2 differential-algebraic equation: large sparse systems in MATLAB

An important component of any initial-value solver for higher-index differential-algebraic equations consists in the computation of consistent initial values. In a recent paper [5], an algorithm is proposed which is applicable to a very general class of index-2 systems. Unfortunately, the computational expense is rather high. We present a modification of this approach, which gives rise to a MATLAB implementation capable of handling systems of moderate dimension (several thousands of unknowns). The algorithm is illustrated by examples.