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SUBROUTINE RKV65B (M,COEFF,QG)
C
C*****************************************************************
C *
C This subroutine determines the coefficients for the embedding *
C formula RKV6(5)9B (method of Verner). *
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. H. Verner : *
C Some Runge-Kutta formular pairs *
C page 496-511 *
C SIAM J. NUMER. ANAL., Vol. 28, No. 2, 1991 *
C *
C*****************************************************************
C
C Declarations
C
DOUBLE PRECISION COEFF(16,M),QG
C
C Initialize QG
C
QG=5.0D0
C
C Determine the matrix elements in COEFF
C
C a - values (see scheme )
C
COEFF(2,1)=1.0D0/8.0D0
COEFF(3,1)=1.0D0/6.0D0
COEFF(4,1)=1.0D0/4.0D0
COEFF(5,1)=1.0D0/2.0D0
COEFF(6,1)=3.0D0/5.0D0
COEFF(7,1)=4.0D0/5.0D0
COEFF(8,1)=1.0D0
COEFF(9,1)=1.0D0
C
C b - values (see scheme)
C
COEFF(2,2)=1.0D0/8.0D0
COEFF(3,2)=1.0D0/18.0D0
COEFF(4,2)=1.0D0/16.0D0
COEFF(5,2)=1.0D0/4.0D0
COEFF(6,2)=134.0D0/625.0D0
COEFF(7,2)=-98.0D0/1875.0D0
COEFF(8,2)=9.0D0/50.0D0
COEFF(9,2)=11.0D0/144.0D0
COEFF(3,3)=1.0D0/9.0D0
COEFF(4,4)=3.0D0/16.0D0
COEFF(5,4)=-3.0D0/4.0D0
COEFF(6,4)=-333.0D0/625.0D0
COEFF(7,4)=12.0D0/625.0D0
COEFF(8,4)=21.0D0/25.0D0
COEFF(5,5)=1.0D0
COEFF(6,5)=476.0D0/625.0D0
COEFF(7,5)=107.36D2/131.25D2
COEFF(8,5)=-2924.0D0/1925.0D0
COEFF(9,5)=256.0D0/693.0D0
COEFF(6,6)=98.0D0/625.0D0
COEFF(7,6)=-1936.0D0/1875.0D0
COEFF(8,6)=74.0D0/25.0D0
COEFF(7,7)=22.0D0/21.0D0
COEFF(8,7)=-15.0D0/7.0D0
COEFF(9,7)=125.0D0/504.0D0
COEFF(8,8)=15.0D0/22.0D0
COEFF(9,8)=125.0D0/528.0D0
COEFF(9,9)=5.0D0/72.0D0
C
C A tilde values (see scheme)
C
COEFF(2,3)=11.0D0/144.0D0
COEFF(2,6)=256.0D0/693.0D0
COEFF(2,8)=125.0D0/504.0D0
COEFF(2,9)=125.0D0/528.0D0
COEFF(3,4)=5.0D0/72.0D0
C
C A - values (see scheme)
C
COEFF(1,1)=1.0D0/18.0D0
COEFF(1,4)=32.0D0/63.0D0
COEFF(1,5)=-2.0D0/3.0D0
COEFF(1,6)=125.0D0/126.0D0
COEFF(1,8)=-5.0D0/63.0D0
COEFF(1,9)=4.0D0/21.0D0
RETURN
END
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