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      SUBROUTINE RK547M (M,COEFF,QG)
C
C*****************************************************************
C                                                                *
C This subroutine determines the coefficients for the embedding  *
C formula RK5(4)7M (method of Dormand und Prince).               *
C                                                                *
C                                                                *
C INPUT PARAMETERS:                                              *
C =================                                              *
C M       : Dimension of the matrix COEFF depending on the chosen*
C           embedding formula                                    *
C                                                                *
C                                                                *
C OUTPUT PARAMETERS:                                             *
C ==================                                             *
C COEFF   : 2-dimensional DOUBLE PRECISION array COEFF(1:16,1:M) *
C           with the coefficients for the embedding formula      *
C QG      : DOUBLE PRECISION value for the global error order    *
C                                                                *
C                                                                *
C----------------------------------------------------------------*
C                                                                *
C  required subroutines: none                                    *
C                                                                *
C*****************************************************************
C                                                                *
C  Author   : Volker Krüger                                      *
C  Date     : 26.04.1993                                         *
C  Source   : FORTRAN 77                                         *
C  Sources  : J. R. Dormand P. J. Prince :                       *
C             A family of embedded Runge-Kutta formulae          *
C             page 19-26                                         *
C             Journal of Computational and Applied Mathematics,  *
C             volume 6, no 1, 1980                               *
C                                                                *
C*****************************************************************
C
C Declarations
C
      DOUBLE PRECISION COEFF(16,M),QG
C
C Initialize QG
C
      QG=4.0D0
C
C Determine the matrix elements in COEFF
C
C         a - values (see scheme )
C
      COEFF(2,1)=1.0D0/5.0D0
      COEFF(3,1)=3.0D0/10.0D0
      COEFF(4,1)=4.0D0/5.0D0
      COEFF(5,1)=8.0D0/9.0D0
      COEFF(6,1)=1.0D0
      COEFF(7,1)=1.0D0
C
C         b - values (see scheme)
C
      COEFF(2,2)=1.0D0/5.0D0
      COEFF(3,2)=3.0D0/40.0D0
      COEFF(4,2)=44.0D0/45.0D0
      COEFF(5,2)=19372.0D0/6561.0D0
      COEFF(6,2)=9017.0D0/3168.0D0
      COEFF(7,2)=35.0D0/384.0D0
      COEFF(3,3)=9.0D0/40.0D0
      COEFF(4,3)=-56.0D0/15.0D0
      COEFF(5,3)=-25360.0D0/2187.0D0
      COEFF(6,3)=-355.0D0/33.0D0
      COEFF(4,4)=32.0D0/9.0D0
      COEFF(5,4)=64448.0D0/6561.0D0
      COEFF(6,4)=46732.0D0/5247.0D0
      COEFF(7,4)=500.0D0/1113.0D0
      COEFF(5,5)=-212.0D0/729.0D0
      COEFF(6,5)=49.0D0/176.0D0
      COEFF(7,5)=125.0D0/192.0D0
      COEFF(6,6)=-5103.0D0/18656.0D0
      COEFF(7,6)=-2187.0D0/6784.0D0
      COEFF(7,7)=11.0D0/84.0D0
C
C         A tilde values (see scheme)
C
      COEFF(2,3)=35.0D0/384.0D0
      COEFF(2,5)=500.0D0/1113.0D0
      COEFF(2,6)=125.0D0/192.0D0
      COEFF(2,7)=-2187.0D0/6784.0D0
      COEFF(3,4)=11.0D0/84.0D0
C
C          A - values (see scheme)
C
      COEFF(1,1)=5179.0D0/57600.0D0
      COEFF(1,3)=7571.0D0/16695.0D0
      COEFF(1,4)=393.0D0/640.0D0
      COEFF(1,5)=-92097.0D0/339200.0D0
      COEFF(1,6)=187.0D0/2100.0D0
      COEFF(1,7)=1.0D0/40.0D0
      RETURN
      END


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