The orders of embedded continuous explicit Runge-Kutta methods

Previously, the authors [9] classified various types of continuous explicit Runge-Kutta methods of order 5. Here, new lower bounds on the numbers of stages required for a sequence of continuous methods of increasing orders which are embedded in a continuouss-stage method of orderp are obtained. Carnicer [2] showed for each continuous explicit Runge-Kutta method of orderp in a mildly restricted family that at least 2p − 2 stages are required. Here, the same bound is established for all such methods of orderp.