for ( j = 1; j <= j_max; j++ ) {
    time_new = j * time_delta;

/* Send H[1] to ID-1. */

    if ( 0 < id ) {
      tag = 1;
      MPI_Send ( &h[1], 1, MPI_DOUBLE, id-1, tag, MPI_COMM_WORLD );
    }
/* Receive H[N+1] from ID+1. */

    if ( id < p-1 ) {
      tag = 1;
      MPI_Recv ( &h[n+1], 1,  MPI_DOUBLE, id+1, tag, MPI_COMM_WORLD, &status );
    }
/* Send H[N] to ID+1. */

    if ( id < p-1 ) {
      tag = 2;
      MPI_Send ( &h[n], 1, MPI_DOUBLE, id+1, tag, MPI_COMM_WORLD );
    }
/* Receive H[0] from ID-1. */

    if ( 0 < id ) {
      tag = 2;
      MPI_Recv ( &h[0], 1, MPI_DOUBLE, id-1, tag, MPI_COMM_WORLD, &status );
    }