Solution of index 2 implicit differential-algebraic equations by Lobatto Runge-Kutta methods

We consider the numerical solution of systems of index 2 implicit differential-algebraic equations (DAEs) by a class of super partitioned additive Runge-Kutta (SPARK) methods. The families of Lobatto IIIA-B-C-C*-D methods are included. We show super-convergence of optimal order 2s-2 for the s-stage Lobatto families provided the constraints are treated in a particular way which strongly relies on specific properties of the SPARK coefficients. Moreover, reversibility properties of the flow can still be preserved provided certain SPARK coefficients are symmetric.