Index 2 differential-algebraic equations play an important role in the modeling of mechanical systems subject to constraints. They are typically expressible in the autonomous Hessenberg form assumed in this paper. The numerical method considered here for their approximate solution is based on a pair of related Runge-Kutta methods, one of which is explicit and is used for the differential components, and the other of which is semi-implicit and is used for the algebraic components. Methods partitioned in this manner have excellent potential as efficient integrators for these difficult problems.

The paper is divided into several parts. The theoretical part deals with the sensitivity of the method to perturbations and establishes a convergence result. Next, the main part deals with the construction of practical and usable methods. The final section presents the results of numerical experiments. These tests indicate that the preferred new method, with fifth-order accuracy, performs well compared with some previously known methods.