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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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