A NEW CLASS OF DISCRETIZATION METHODS FOR THE SOLUTION OF LINEAR DIFFERENTIAL-ALGEBRAIC EQUATIONS WITH VARIABLE-COEFFICIENTS

We discuss new discretization methods for linear differential-algebrai c equations (DAEs) with variable coefficients. We introduce numerical methods to compute the local invariants of such DAEs that were introdu ced by the authors in a previous paper [P. Kunkel and V. Mehrmann, J. Comput. Appl. Math., 56 (1994), pp. 225-251]. Using these quantities w e are able to determine numerically global invariances like the strang eness index, which generalizes the differentiation index for DAEs that in particular include undetermined solution components. Based on thes e methods we then obtain regularization schemes, which allow us to emp loy general solution methods. The new methods are tested on a number o f numerical examples.