Partitioned Runge-Kutta Methods for Semi-explicit Differential-Algebraic Systems of Index 2

A general class of one-step methods for index 2 differential-algebraic systems in Hessenberg form is studied. This family of methods, which we call partitioned Runge-Kutta methods, includes all one-step methods of Runge-Kutta type proposed in the literature for integrating such DAE systems, including the more recently proposed classes of half-explicit methods. A new family of super-convergent partitioned Runge-Kutta methods based on Gauss methods is presented. A detailed theoretical study of partitioned Runge-Kutta methods that exactly satisfy the original algebraic constraint of the DAE system is given. In particular, methods with different order of convergence for the differential variables and the algebraic variables are also studied using a graph theoretical approach.