PARALLEL INTERPOLATION OF HIGH-ORDER RUNGE-KUTTA METHODS

Interpolation of high-order Runge-Kutta formulas is always theoretically possible, but in practice it is still unsatisfactory for its expensiveness. In this paper, rather than trying to improve the efficiency, we concentrate our attention to the possibility of using parallelism to improve reliability and functionality. Nevertheless, as we shall see, some modest speedup can also be gained. As an illustration, our approach is applied to the well-known RK8(7) pair of Prince and Dormand [10], and its speedup and efficiency examined. Numerical experimentation using the nonstiff package of test problems by Enright and Pryce [4] shows the very good performance of the technique proposed.