Convergence of Lobatto-type Runge-Kutta methods for partitioned differential-algebraic systems of index 2

Abstract

In this paper we propose a numerical scheme for partitioned systems of index 2 DAEs, such as those arising from nonholonomic mechanical problems and prove the order of a certain class of Runge-Kutta methods we call of Lobatto-type. The study of nonholonomic systems has recently shown a new interest in that theory and also in its relation to the new developments in control theory, subriemannian geometry, robotics, etc. The proofs and general outline of the paper follow a similar procedure of the one by L.O. Jay in the non-partitioned setting, but we tackle the issue of having two different sets of coefficients in interaction.