The paper illustrates the use of parallel processing to simulate dynamical systems described by a complex high-dimensional set of ordinary differential equations. A substantial paradigm problem is drawn from the nuclear industry to illustrate the use of an integrated parallel processing methodology. This includes heuristic rules for algorithm and architecture selection, a classification for decomposition techniques, and their use in a well known and structured top-down approach. A new (parallel) version of the Davison–Cross stiff system solver is introduced and used in five different parallel processing configurations. Significant benefits owing to the extensive use of parallel emulation techniques to iteratively propose and refine candidate parallel processing solutions are highlighted.