Abstract
Parallel block methods with a stepsize strategy are developed for solving nonstiff initial value problems on parallel computers. The block methods use the predictor-corrector iteration, which makes it easy to exploit "parallelism across the method" for the solutions of nonlinear equations. The stepsize strategy used in the methods is based on Milne's device which estimates the local error using the predicted and corrected values. Numerical experiments are carried out on a KSR1 parallel computer in order to show the performance of the block methods. The computational costs, errors and speed-up ratios of the block methods are compared with those of the PIRK(parallel iterated Runge-Kutta) by Houwen et al.
