Parallel solution in space of large ODEs using block multistep method with step size controller

The parallel 4-point implicit multistep block method is developed for solving large system of first order ODEs using variable step size. The proposed method computes the numerical solution at four points simultaneously. The Gauss Seidel style is used for the implementation of the method. The parallelism across the system is considered for the parallelization of the method and parallel version has been implemented using MPI communication environment on a High Performance Computer (HPC). The results indicate the advantage of utilizing the parallel implementation of the proposed method for solving large-scale system of ODEs.