Parallel predictor-corrector methods

In this paper we construct predictor-corrector methods using block Runge-Kutta methods as correctors. Like conventional Runge-Kutta methods, these correctors compute stage values at non-uniformly distributed, intermediate points. The predictor-corrector nature of the methods make them suitable for implementation on parallel computers. Comparisons of an 8th-order, 5-processor predictor-corrector method using Radau II points with the celebrated 8(7) Runge-Kutta method of Prince and Dormand show speed-up factors from 1.9 until 2.9.