In this paper, we propose a fast convergence parallel iteration process for solving a low-order
implicit Runge-Kutta-Nystr??m method. The resulting scheme can be regarded as a parallel singly
diagonally implicit Runge-Kutta-Nystr??m (PDIRKN) method. On a two-processor computer, this parallel
method requires effectively two sequential implicit stages per step. By numerical experiments applied to
initial-boundary-value problems for semi-discrete partial differential equations (PDEs), we compare this
method with some sequential DIRKN methods from the literature, and show its efficiency in a low-accuracy
range which is realistic for these problems. ?? 1995.
