The MPI is the most widespread data exchange interface standard used in parallel programming for clusters and supercomputers with many computer platforms. The primary means of the MPI communication between processes is passing messages based on basic point-to-point blocking and non-blocking routines. The choice of the optimal implementation of exchanges is essential to minimize the idle and transmission times to achieve parallel algorithm efficiency. We used three realizations of data exchange processes based on blocking, non-blocking point-to-point MPI routines and new features of the Coarray Fortran technique to determine the most efficient parallelization strategy. For the study, the two-dimensional wave equation was used as a test problem. During the experiments, the problem size and the approaches to the data exchange for transferring data between processes were changed. For each version, we measured the computation time and the acceleration factor. The research carried out shows that the larger the problem size, the greater the benefits of delayed non-blocking routines and Coarray Fortran. The efficiency of delayed non-blocking operations is due to overlapping the data transfer in the computations background. The Coarray Fortran acceleration is achieved by using Coarray variables with shared memory. The Coarray approach starts to win with the growth of problem size.