This paper describes the construction of block predictor-corrector methods based on Runge-Kutta-
Nystr??m correctors. Our approach is to apply the predictor-corrector method not only with stepsize h, but,
in addition (and simultaneously) with stepsizes aih, i = 1, . . . , r. In this way, at each step, a whole block of
approximations to the exact solution at off-step points is computed. In the next step, these approximations
are used to obtain a high-order predictor formula using Lagrange or Hermite interpolation. Since the block
approximations at the off-step points can be computed in parallel, the sequential costs of these block
predictor-corrector methods are comparable with those of a conventional predictor-corrector method.
Furthermore, by using Runge-Kutta-Nystr??m corrector methods, the computation of the approximation at
each off-step point is also highly parallel. Numerical comparisons on a shared memory computer show the
efficiency of the methods for problems with expensive function evaluations. ?? J.C. Baltzer AG, Science
Publishers.
