CWI CONTRIBUTIONS TO THE DEVELOPMENT OF PARALLEL RUNGE-KUTTA METHODS

This paper will concentrate on contributions of CWI to the development of parallel Runge-Kutta (RK) methods. We shall describe two approache s to construct such methods. In both approaches, a conventional implic it RK method is used as a corrector equation whose solution is approxi mated by an iterative method. In the first approach, the iteration met hod uses a fixed number of iterations without solving the corrector. A ssuming that a one-step predictor is used, this approach again results in an RK method, however, an RK method possessing a lot of intrinsic parallelism. In the second approach, the corrector is solved by modifi ed Newton iteration and the linear systems arising in each Newton iter ation are solved by a parallel iteration process which is tuned to the special form of these linear systems. Furthermore, we apply the paral lel iteration process in a step-parallel fashion which further enhance s the amount of parallelism. Finally, the application of parallel RK m ethods within the framework of waveform relaxation is briefly discusse d.