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SUBROUTINE RKV65 (M,COEFF,QG)
C
C*****************************************************************
C *
C This subroutine determines the coefficients for the embedding *
C formula RKV6(5) (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 Explicit Runge-Kutta methods with estimates of *
C the local truncation error *
C page 772-790 *
C SIAM J. NUMER. ANAL., Vol. 15, No. 4, 1978 *
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)=1.0D0/18.0D0
COEFF(3,1)=1.0D0/6.0D0
COEFF(4,1)=2.0D0/9.0D0
COEFF(5,1)=2.0D0/3.0D0
COEFF(6,1)=1.0D0
COEFF(7,1)=8.0D0/9.0D0
COEFF(8,1)=1.0D0
C
C b - values (see scheme)
C
COEFF(2,2)=1.0D0/18.0D0
COEFF(3,2)=-1.0D0/12.0D0
COEFF(4,2)=-2.0D0/81.0D0
COEFF(5,2)=40.0D0/33.0D0
COEFF(6,2)=-369.0D0/73.0D0
COEFF(7,2)=-8716.0D0/891.0D0
COEFF(8,2)=3015.0D0/256.0D0
COEFF(3,3)=1.0D0/4.0D0
COEFF(4,3)=4.0D0/27.0D0
COEFF(5,3)=-4.0D0/11.0D0
COEFF(6,3)=72.0D0/73.0D0
COEFF(7,3)=656.0D0/297.0D0
COEFF(8,3)=-9.0D0/4.0D0
COEFF(4,4)=8.0D0/81.0D0
COEFF(5,4)=-56.0D0/11.0D0
COEFF(6,4)=5380.0D0/219.0D0
COEFF(7,4)=39520.0D0/891.0D0
COEFF(8,4)=-4219.0D0/78.0D0
COEFF(5,5)=54.0D0/11.0D0
COEFF(6,5)=-122.85D2/584.0D0
COEFF(7,5)=-416.0D0/11.0D0
COEFF(8,5)=5985.0D0/128.0D0
COEFF(6,6)=2695.0D0/1752.0D0
COEFF(7,6)=52.0D0/27.0D0
COEFF(8,6)=-539.0D0/384.0D0
COEFF(8,8)=693.0D0/3328.0D0
C
C A tilde values (see scheme)
C
COEFF(2,3)=57.0D0/640.0D0
COEFF(2,5)=-16.0D0/65.0D0
COEFF(2,6)=1377.0D0/2240.0D0
COEFF(2,7)=121.0D0/320.0D0
COEFF(3,4)=891.0D0/8320.0D0
COEFF(3,5)=2.0D0/35.0D0
C
C A - values (see scheme)
C
COEFF(1,1)=3.0D0/80.0D0
COEFF(1,3)=4.0D0/25.0D0
COEFF(1,4)=243.0D0/1120.0D0
COEFF(1,5)=77.0D0/160.0D0
COEFF(1,6)=73.0D0/700.0D0
RETURN
END
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