Partitioned half-explicit Runge-Kutta methods for differential-algebraic systems of index 2

A class of half-explicit methods for index 2 differential-algebraic systems in Hessenberg form is proposed, which takes advantage of the partitioned structure of such problems. For this family of methods, which we call partitioned half-explicit Runge-Kutta methods, a better choice in the parameters of the method than for previously available half-explicit Runge-Kutta methods can be made. In particular we construct a family of 6-stage methods of order 5, and determine its parameters (based on the coefficients of the successful explicit Runge-Kutta method DOPRI5) in order to optimize the local error coefficients. Numerical experiments demonstrate the efficiency of this method for the solution of constrained multi-body systems.