Parallelizing a fourth-order Runge-Kutta method

The most commonly used fourth-order Runge-Kutta(RK) method ip examined for its suitability for parallelization. To avoid the inherent data dependence, parallelization of the BK method uses some iterations that deviate from the traditional method. Numerical results have been obtained for comparison between parallel end serial programs, and comparison with known exact solutions. The RK method is found to be parallelizable for only a snail number of processors. A step control method that allows a half- or double-step sizing at run time is parallelizable for up to four processors. Serial and parallel programs are written in Fortran 90. The parallel program has a Message Passing Interface(MPI version and a High Performance Portran(HPF) version. The parallel methods decrease accuracy without significant gains of efficiency. When applicable, an application should be parallelized at the level calling the Runge-Kutta subroutine, with each RK invocation executed serially.