End of file
Contents
Index

      SUBROUTINE RK547C (M,COEFF,QG)
C
C*****************************************************************
C                                                                *
C This subroutine determines the coefficients for the embedding  *
C formula RK5(4)7C (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=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)=6.0D0/13.0D0
      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)=1.0D0/5.0D0
      COEFF(3,2)=3.0D0/40.0D0
      COEFF(4,2)=264.0D0/2197.0D0
      COEFF(5,2)=932.0D0/3645.0D0
      COEFF(6,2)=-367.0D0/513.0D0
      COEFF(7,2)=35.0D0/432.0D0
      COEFF(3,3)=9.0D0/40.0D0
      COEFF(4,3)=-90.0D0/2197.0D0
      COEFF(5,3)=-14.0D0/27.0D0
      COEFF(6,3)=30.0D0/19.0D0
      COEFF(4,4)=840.0D0/2197.0D0
      COEFF(5,4)=3256.0D0/5103.0D0
      COEFF(6,4)=9940.0D0/5643.0D0
      COEFF(7,4)=8500.0D0/14553.0D0
      COEFF(5,5)=7436.0D0/25515.0D0
      COEFF(6,5)=-29575.0D0/8208.0D0
      COEFF(7,5)=-28561.0D0/84672.0D0
      COEFF(6,6)=6615.0D0/3344.0D0
      COEFF(7,6)=405.0D0/704.0D0
      COEFF(7,7)=19.0D0/196.0D0
C
C         A tilde values (see scheme)
C
      COEFF(2,3)=35.0D0/432.0D0
      COEFF(2,5)=8500.0D0/14553.0D0
      COEFF(2,6)=-28561.0D0/84672.0D0
      COEFF(2,7)=405.0D0/704.0D0
      COEFF(3,4)=19.0D0/196.0D0
C
C          A - values (see scheme)
C
      COEFF(1,1)=11.0D0/108.0D0
      COEFF(1,3)=6250.0D0/14553.0D0
      COEFF(1,4)=-2197.0D0/21168.0D0
      COEFF(1,5)=81.0D0/176.0D0
      COEFF(1,6)=171.0D0/1960.0D0
      COEFF(1,7)=1.0D0/40.0D0
      RETURN
      END


Begin of file
Contents
Index