Specialized Partitioned Additive Runge-Kutta Methods for Systems of Overdetermined DAEs with Holonomic Constraints

Abstract. We consider a general class of systems of overdetermined differential-algebraic equations (ODAEs). We are particularly interested in extending the application of the symplectic Gauss methods to Hamiltonian and Lagrangian systems with holonomic constraints. For the numerical approximation to the solution to these ODAEs, we present specialized partitioned additive Runge– Kutta (SPARK) methods, and in particular the new class of (s, s)-Gauss–Lobatto SPARK methods. These methods not only preserve the constraints, symmetry, symplecticness of the flow, and variational nature of the trajectories of holonomically constrained Hamiltonian and Lagrangian systems, but they also have an optimal order of convergence 2s.