Partitioned half-explicit Runge-Kutta methods for differential-algebraic system of index 2 (Q1365538)

The author considers the initial value problem for semi-explicit differential-algebraic systems of index 2. For the numerical solution of this problem, he proposes a class of partitioned half-explicit Runge-Kutta methods. The methods compute at each step approximations of the solution for the \(y\)-component and also for the \(z\)-component. A few statements express the local uniqueness of the solution of the Runge-Kutta equations and the order of convergence of the numerical method. Some particular methods of order 4, 5 and 6 are derived and also one four-order continuous approximation. Numerical experiments are made on multibody systems.