Optimized explicit Runge-Kutta pair of orders 9(8)

A fully explicit algorithm for deriving a Runge-Kutta pair of orders 9(8) is presented in this paper. After that an optimal pair is given, which is found to outperform all other published Runge-Kutta pairs when severe tolerances are required. (C) 2001 IMACS. Published by Elsevier Science B.V. All rights reserved.