A parallel DIRK method for stiff initial-value problems

Abstract

In this note we propose a fast parallel iteration process for solving a low-order implicit Runge- Kutta method. The resulting scheme can be regarded as a parallel singly diagonally implicit Runge-Kutta (PDIRK) method. On a two-processor computer, this method requires effectively the solution of two implicit relations per step. By two numerical experiments we compare this method with some sequential methods from the literature, and show its efficient behaviour. ?? 1994.