A FAST CONVERGENCE PARALLEL DIRKN METHOD AND ITS APPLICATIONS TO PDES

In this paper, we propose a fast convergence parallel iteration proces s for solving a low-order implicit Runge-Kutta-Nystrom method. The res ulting scheme can be regarded as a parallel singly diagonally implicit Runge-Kutta-Nystrom (PDIRKN) method. On a two-processor computer, thi s parallel method requires effectively two sequential implicit stages per step. By numerical experiments applied to initial-boundary-value p roblems for semi-discrete pai tial differential equations (PDEs), we c ompare this method with some sequential DIRKN methods from the literat ure, and show its efficiency in a low-accuracy range which is realisti c for these problems.