Parallelism across the methodWe have adopted a technique to determine the degree of the parallelism of a given method similar to the digraph method used for Runge-Kutta methods.
The degree of parallelism of an arbitrary numerical method for the solution of ODEs can be easily estimated with EpODE. Each equation of the iterative procedure associated with the numerical method is analyzed and a data flow graph is determined. This graph is divided into stages and processes in a similar manner with the level-process partitioning proposed for Runge-Kutta methods. If the expert decides that it is possible to use more than one process and we use the option Solve -> Multiprocessor code -> Method distribution, then the expert will create an appropriate number of processes.
At a particular stage, each process is responsible for the solution of one or more method equations. These equations are to be changed from each stage to another, but, at a particular stage number, the equations distributed to a process are the same at each integration step.