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      SUBROUTINE RK547S (M,COEFF,QG)
C
C*****************************************************************
C                                                                *
C This subroutine determines the coefficients for the embedding  *
C formula RK5(4)7S (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)=2.0D0/9.0D0
      COEFF(3,1)=1.0D0/3.0D0
      COEFF(4,1)=5.0D0/9.0D0
      COEFF(5,1)=2.0D0/3.0D0
      COEFF(6,1)=1.0D0
      COEFF(7,1)=1.0D0
C
C         b - values (see scheme)
C
      COEFF(2,2)=2.0D0/9.0D0
      COEFF(3,2)=1.0D0/12.0D0
      COEFF(4,2)=55.0D0/324.0D0
      COEFF(5,2)=83.0D0/330.0D0
      COEFF(6,2)=-19.0D0/28.0D0
      COEFF(7,2)=19.0D0/200.0D0
      COEFF(3,3)=1.0D0/4.0D0
      COEFF(4,3)=-25.0D0/108.0D0
      COEFF(5,3)=-13.0D0/22.0D0
      COEFF(6,3)=9.0D0/4.0D0
      COEFF(4,4)=50.0D0/81.0D0
      COEFF(5,4)=61.0D0/66.0D0
      COEFF(6,4)=1.0D0/7.0D0
      COEFF(7,4)=3.0D0/5.0D0
      COEFF(5,5)=9.0D0/110.0D0
      COEFF(6,5)=-27.0D0/7.0D0
      COEFF(7,5)=-243.0D0/400.0D0
      COEFF(6,6)=22.0D0/7.0D0
      COEFF(7,6)=33.0D0/40.0D0
      COEFF(7,7)=7.0D0/80.0D0
C
C         A tilde values (see scheme)
C
      COEFF(2,3)=19.0D0/200.0D0
      COEFF(2,5)=3.0D0/5.0D0
      COEFF(2,6)=-243.0D0/400.0D0
      COEFF(2,7)=33.0D0/40.0D0
      COEFF(3,4)=7.0D0/80.0D0
C
C          A - values (see scheme)
C
\hbox{\JDhspace\verb`
      COEFF(1,1)=431.0D0/5000.0D0
      COEFF(1,3)=333.0D0/500.0D0
      COEFF(1,4)=-7857.0D0/10000.0D0
      COEFF(1,5)=957.0D0/1000.0D0
      COEFF(1,6)=193.0D0/2000.0D0
      COEFF(1,7)=-1.0D0/50.0D0
      RETURN
      END


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