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SUBROUTINE RKF87 (M,COEFF,QG)
C
C*****************************************************************
C *
C This subroutine determines the coefficients for the embedding *
C formula RKF8(7) (method of Fehlberg). *
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 : E. Fehlberg : *
C Klassische Runge-Kutta-Formeln fünfter und *
C siebenter Ordnung mit Schrittweiten-Kontrolle *
C page 93-106 *
C Computing 4 1969 *
C *
C*****************************************************************
C
C Declarations
C
DOUBLE PRECISION COEFF(16,M),QG
C
C Initialize QG
C
QG=7.0D0
C
C Determine the matrix elements in COEFF
C
C a - values (see scheme)
C
COEFF(2,1)=2.0D0/27.0D0
COEFF(3,1)=1.0D0/9.0D0
COEFF(4,1)=1.0D0/6.0D0
COEFF(5,1)=5.0D0/12.0D0
COEFF(6,1)=1.0D0/2.0D0
COEFF(7,1)=5.0D0/6.0D0
COEFF(8,1)=1.0D0/6.0D0
COEFF(9,1)=2.0D0/3.0D0
COEFF(10,1)=1.0D0/3.0D0
COEFF(11,1)=1.0D0
COEFF(13,1)=1.0D0
C
C b - values (see scheme)
C
COEFF(2,2)=2.0D0/27.0D0
COEFF(3,2)=1.0D0/36.0D0
COEFF(4,2)=1.0D0/24.0D0
COEFF(5,2)=5.0D0/12.0D0
COEFF(6,2)=1.0D0/20.0D0
COEFF(7,2)=-25.0D0/108.0D0
COEFF(8,2)=31.0D0/300.0D0
COEFF(9,2)=2.0D0
COEFF(10,2)=-91.0D0/108.0D0
COEFF(11,2)=2383.0D0/4100.0D0
COEFF(12,2)=3.0D0/205.0D0
COEFF(13,2)=-1777.0D0/4100.0D0
COEFF(3,3)=1.0D0/12.0D0
COEFF(4,4)=1.0D0/8.0D0
COEFF(5,4)=-25.0D0/16.0D0
COEFF(5,5)=25.0D0/16.0D0
COEFF(6,5)=1.0D0/4.0D0
COEFF(7,5)=125.0D0/108.0D0
COEFF(9,5)=-53.0D0/6.0D0
COEFF(10,5)=23.0D0/108.0D0
COEFF(11,5)=-341.0D0/164.0D0
COEFF(13,5)=-341.0D0/164.0D0
COEFF(6,6)=1.0D0/5.0D0
COEFF(7,6)=-65.0D0/27.0D0
COEFF(8,6)=61.0D0/225.0D0
COEFF(9,6)=704.0D0/45.0D0
COEFF(10,6)=-976.0D0/135.0D0
COEFF(11,6)=4496.0D0/1025.0D0
COEFF(13,6)=4496.0D0/1025.0D0
COEFF(7,7)=125.0D0/54.0D0
COEFF(8,7)=-2.0D0/9.0D0
COEFF(9,7)=-107.0D0/9.0D0
COEFF(10,7)=311.0D0/54.0D0
COEFF(11,7)=-301.0D0/82.0D0
COEFF(12,7)=-6.0D0/41.0D0
COEFF(13,7)=-289.0D0/82.0D0
COEFF(8,8)=13.0D0/900.0D0
COEFF(9,8)=67.0D0/90.0D0
COEFF(10,8)=-19.0D0/60.0D0
COEFF(11,8)=2133.0D0/4100.0D0
COEFF(12,8)=-3.0D0/205.0D0
COEFF(13,8)=2193.0D0/4100.0D0
COEFF(9,9)=3.0D0
COEFF(10,9)=17.0D0/6.0D0
COEFF(11,9)=45.0D0/82.0D0
COEFF(12,9)=-3.0D0/41.0D0
COEFF(13,9)=51.0D0/82.0D0
COEFF(10,10)=-1.0D0/12.0D0
COEFF(11,10)=45.0D0/164.0D0
COEFF(12,10)=3.0D0/41.0D0
COEFF(13,10)=33.0D0/164.0D0
COEFF(11,11)=18.0D0/41.0D0
COEFF(12,11)=6.0D0/41.0D0
COEFF(13,11)=12.0D0/41.0D0
COEFF(13,13)=1.0D0
C
C A tilde values (see scheme)
C
COEFF(2,8)=34.0D0/105.0D0
COEFF(2,9)=9.0D0/35.0D0
COEFF(2,10)=9.0D0/35.0D0
COEFF(2,11)=9.0D0/280.0D0
COEFF(2,12)=9.0D0/280.0D0
COEFF(3,4)=41.0D0/840.0D0
COEFF(3,5)=41.0D0/840.0D0
C
C A - values (see scheme)
C
COEFF(1,1)=41.0D0/840.0D0
COEFF(1,6)=34.0D0/105.0D0
COEFF(1,7)=9.0D0/35.0D0
COEFF(1,8)=9.0D0/35.0D0
COEFF(1,9)=9.0D0/280.0D0
COEFF(1,10)=9.0D0/280.0D0
COEFF(1,11)=41.0D0/840.0D0
RETURN
END
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