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SUBROUTINE RK547M (M,COEFF,QG)
C
C*****************************************************************
C *
C This subroutine determines the coefficients for the embedding *
C formula RK5(4)7M (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)=4.0D0/5.0D0
COEFF(5,1)=8.0D0/9.0D0
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)=44.0D0/45.0D0
COEFF(5,2)=19372.0D0/6561.0D0
COEFF(6,2)=9017.0D0/3168.0D0
COEFF(7,2)=35.0D0/384.0D0
COEFF(3,3)=9.0D0/40.0D0
COEFF(4,3)=-56.0D0/15.0D0
COEFF(5,3)=-25360.0D0/2187.0D0
COEFF(6,3)=-355.0D0/33.0D0
COEFF(4,4)=32.0D0/9.0D0
COEFF(5,4)=64448.0D0/6561.0D0
COEFF(6,4)=46732.0D0/5247.0D0
COEFF(7,4)=500.0D0/1113.0D0
COEFF(5,5)=-212.0D0/729.0D0
COEFF(6,5)=49.0D0/176.0D0
COEFF(7,5)=125.0D0/192.0D0
COEFF(6,6)=-5103.0D0/18656.0D0
COEFF(7,6)=-2187.0D0/6784.0D0
COEFF(7,7)=11.0D0/84.0D0
C
C A tilde values (see scheme)
C
COEFF(2,3)=35.0D0/384.0D0
COEFF(2,5)=500.0D0/1113.0D0
COEFF(2,6)=125.0D0/192.0D0
COEFF(2,7)=-2187.0D0/6784.0D0
COEFF(3,4)=11.0D0/84.0D0
C
C A - values (see scheme)
C
COEFF(1,1)=5179.0D0/57600.0D0
COEFF(1,3)=7571.0D0/16695.0D0
COEFF(1,4)=393.0D0/640.0D0
COEFF(1,5)=-92097.0D0/339200.0D0
COEFF(1,6)=187.0D0/2100.0D0
COEFF(1,7)=1.0D0/40.0D0
RETURN
END
Begin of file
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