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      SUBROUTINE RK658S (M,COEFF,QG)
C
C*****************************************************************
C                                                                *
C This subroutine determines the coefficients for the embedding  *
C formula RK6(5)8S (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 reconsideration of some embedded Runge Kutta     *
C             formulae                                           *
C             page 203-211                                       *
C             Journal of Computational and Applied Mathematics,  *
C             15, 1986, North-Holland                            *
C                                                                *
C*****************************************************************
C
C Declarations
C
      DOUBLE PRECISION COEFF(16,M),QG
C
C Initialize QG
C
      QG=5.0D0
C
C Determine the matrix elements in COEFF
C
C         a - values (see scheme )
C
      COEFF(2,1)=1.0D0/4.0D0
      COEFF(3,1)=3.0D0/10.0D0
      COEFF(4,1)=6.0D0/7.0D0
      COEFF(5,1)=3.0D0/5.0D0
      COEFF(6,1)=4.0D0/5.0D0
      COEFF(7,1)=1.0D0
      COEFF(8,1)=1.0D0
C
C         b - values (see scheme)
C
      COEFF(2,2)=1.0D0/4.0D0
      COEFF(3,2)=3.0D0/25.0D0
      COEFF(4,2)=102.0D0/343.0D0
      COEFF(5,2)=-3.0D0/100.0D0
      COEFF(6,2)=37.0D0/225.0D0
      COEFF(7,2)=11.0D0/648.0D0
      COEFF(8,2)=796.0D0/1701.0D0
      COEFF(3,3)=9.0D0/50.0D0
      COEFF(4,3)=-1368.0D0/343.0D0
      COEFF(5,3)=36.0D0/25.0D0
      COEFF(6,3)=-48.0D0/25.0D0
      COEFF(7,3)=14.0D0/3.0D0
      COEFF(8,3)=-352.0D0/63.0D0
      COEFF(4,4)=1560.0D0/343.0D0
      COEFF(5,4)=-12.0D0/13.0D0
      COEFF(6,4)=872.0D0/351.0D0
      COEFF(7,4)=-10193.0D0/2106.0D0
      COEFF(8,4)=134096.0D0/22113.0D0
      COEFF(5,5)=147.0D0/1300.0D0
      COEFF(6,5)=49.0D0/1053.0D0
      COEFF(7,5)=-30331.0D0/50544.0D0
      COEFF(8,5)=-78281.0D0/75816.0D0
      COEFF(6,6)=2.0D0/81.0D0
      COEFF(7,6)=1025.0D0/1944.0D0
      COEFF(8,6)=-9425.0D0/20412.0D0
      COEFF(7,7)=59.0D0/48.0D0
      COEFF(8,7)=781.0D0/504.0D0
C
C         A tilde values (see scheme)
C
      COEFF(2,3)=29.0D0/324.0D0
      COEFF(2,5)=3400.0D0/7371.0D0
      COEFF(2,6)=-16807.0D0/25272.0D0
      COEFF(2,7)=-125.0D0/1944.0D0
      COEFF(2,8)=25.0D0/24.0D0
      COEFF(3,4)=1.0D0/84.0D0
      COEFF(3,5)=1.0D0/8.0D0
C
C          A - values (see scheme)
C
      COEFF(1,1)=2041.0D0/21600.0D0
      COEFF(1,3)=748.0D0/1755.0D0
      COEFF(1,4)=-2401.0D0/46800.0D0
      COEFF(1,5)=11.0D0/108.0D0
      COEFF(1,6)=59.0D0/160.0D0
      COEFF(1,7)=3.0D0/50.0D0
      RETURN
      END


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