|
Abstract:
|
The aim of the present paper is to construct a class of two-step Runge-Kutta methods of arbitrarily
high order for application to parallel computers. Starting with an s-stage implicit two-step Runge-Kutta
method of order p with k = p/2 implicit stages, we apply the highly parallel predictor-corrector iteration
process in P(EC)mE mode. In this way, we obtain an explicit two-step Runge-Kutta method that has order p
for all m and that requires k(m + 1) right-hand side evaluations per step of which each k evaluation can be
computed in parallel. By a number of numerical experiments we show the superiority of the parallel
predictor-corrector methods proposed here over parallel methods available in the literature. |