End of file
Contents
Index

      SUBROUTINE RK546M (M,COEFF,QG)
C
C*****************************************************************
C                                                                *
C This subroutine determines the coefficients for the embedding  *
C formula RK5(4)6M (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)=3.0D0/5.0D0
      COEFF(5,1)=2.0D0/3.0D0
      COEFF(6,1)=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)=3.0D0/10.0D0
      COEFF(5,2)=226.0D0/729.0D0
      COEFF(6,2)=-181.0D0/270.0D0
      COEFF(3,3)=9.0D0/40.0D0
      COEFF(4,3)=-9.0D0/10.0D0
      COEFF(5,3)=-25.0D0/27.0D0
      COEFF(6,3)=5.0D0/2.0D0
      COEFF(4,4)=6.0D0/5.0D0
      COEFF(5,4)=880.0D0/729.0D0
      COEFF(6,4)=-266.0D0/297.0D0
      COEFF(5,5)=55.0D0/729.0D0
      COEFF(6,5)=-91.0D0/27.0D0
      COEFF(6,6)=189.0D0/55.0D0
C
C         A tilde values (see scheme)
C
      COEFF(2,3)=19.0D0/216.0D0
      COEFF(2,5)=1000.0D0/2079.0D0
      COEFF(2,6)=-125.0D0/216.0D0
      COEFF(3,4)=81.0D0/88.0D0
      COEFF(3,5)=5.0D0/56.0D0
C
C          A - values (see scheme)
C
      COEFF(1,1)=31.0D0/540.0D0
      COEFF(1,3)=190.0D0/297.0D0
      COEFF(1,4)=-145.0D0/108.0D0
      COEFF(1,5)=351.0D0/220.0D0
      COEFF(1,6)=1.0D0/20.0D0
      RETURN
      END


Begin of file
Contents
Index