A fast convergence parallel DIRKN method and its applications to PDEs Original Research Article

In this paper, we propose a fast convergence parallel iteration process for solving a low-order implicit Runge-Kutta-Nyström method. The resulting scheme can be regarded as a parallel singly diagonally implicit Runge-Kutta-Nyström (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.