PARTITIONED HALF-EXPLICIT RUNGE-KUTTA METHODS FOR DIFFERENTIAL-ALGEBRAIC SYSTEMS OF INDEX 2

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