Computation of consistent initial values for properly stated index 3 DAEs

The computation of consistent initial values is one of the basic problems when solving initial or boundary value problems of DAEs. For a given DAE it is, in fact, not obvious how to formulate the initial conditions that lead to a uniquely solvable IVP. The existing algorithms for the solution of this problem are either designed for fixed index, or they require a special structure of the DAE or they need more than the given data (e.g. additional differentiations). In this paper, combining the results concerning the solvability of DAEs with properly stated leading terms with an appropriate method for the approximation of the derivative, we propose an algorithm that provides the necessary data to formulate the initial conditions and which works at least for nonlinear DAEs up to index 3. Illustrative examples are given.