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 at step points, but
also at off-step points (block points), so that in 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 interpolation. By suitable choice of the abscissas of the off-step points, a
much more accurately predicted value is obtained than by predictor formulas based on last step values. Since
the block of 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. Application of the resulting block predictor-corrector methods to a
few widely-used test problems reveals that the sequential costs are reduced by a factor ranging from 4 to 50
when compared with the best sequential methods from the literature.
