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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
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