Multiprocessor implementations of a parallel Implicit Runge-Kutta code

A two-stage Implicit Runge-Kutta algorithm is shown to exhibit a high level of parallelism making it an ideal candidate for coding and execution on a two-processor parallel computing system. The algorithm is coded for execution on both a loosely-coupled (CDC Cyberplus) and a tightly-coupled (CRI Cray X-MP) multiprocessor system. The coding and implementation on both systems is described and the performance in terms of speedup is presented. It is shown that the algorithm may be successfully parallel processed on the tightly-coupled system.