Half-explicit Runge{kutta Methods with Explicit Stages for Diierential-algebraic Systems of Index 2

Usually the straightforward generalization of explicit Runge{Kutta methods for ordinary diierential equations to half-explicit methods for diierential-algebraic systems of index 2 results in methods of order q 2 ((8]). The construction of higher order methods is simpliied substantially by a slight modiication of the method combined with an improved strategy for the computation of the algebraic solution components. We give order conditions up to order q = 5 and study the convergence of these methods. Based on the fth order method of Dormand and Prince a half-explicit Runge{Kutta method of order q = 5 is constructed that requires the solution of 6 systems of nonlinear equations per step of integration.