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-algebraic equations (DAEs) with variable coefficients. We introduce numerical methods to compute the local invariants of such DAEs that were introduced by the authors in a previous paper [P. Kunkel and V Mehrmann, J. Comput. Appl. Math., 56 (1994), pp. 225–251]. Using these quantities we are able to determine numerically global invariances like the strangeness index, which generalizes the differentiation index for DAEs that in particular include undetermined solution components. Based on these methods we then obtain regularization schemes, which allow us to employ general solution methods. The new methods are tested on a number of numerical examples.