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SUBROUTINE RKV76 (M,COEFF,QG)
C
C*****************************************************************
C *
C This subroutine determines the coefficients for the embedding *
C formula RKV7(6) (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=6.0D0
C
C Determine the matrix elements in COEFF
C
C a - values (see scheme )
C
COEFF(2,1)=1.0D0/12.0D0
COEFF(3,1)=1.0D0/6.0D0
COEFF(4,1)=1.0D0/4.0D0
COEFF(5,1)=3.0D0/4.0D0
COEFF(6,1)=16.0D0/17.0D0
COEFF(7,1)=1.0D0/2.0D0
COEFF(8,1)=1.0D0
COEFF(9,1)=2.0D0/3.0D0
COEFF(10,1)=1.0D0
C
C b - values (see scheme)
C
COEFF(2,2)=1.0D0/12.0D0
COEFF(4,2)=1.0D0/16.0D0
COEFF(5,2)=21.0D0/16.0D0
COEFF(6,2)=1344.688D3/2505.63D2
COEFF(7,2)=-559.0D0/384.0D0
COEFF(8,2)=-625.0D0/224.0D0
COEFF(9,2)=-1225.3D1/9914.4D1
COEFF(10,2)=3051.7D1/2512.0D0
COEFF(3,3)=1.0D0/6.0D0
COEFF(4,4)=3.0D0/16.0D0
COEFF(5,4)=-81.0D0/16.0D0
COEFF(6,4)=-1709.184D3/8352.1D1
COEFF(7,4)=6.0D0
COEFF(8,4)=12.0D0
COEFF(9,4)=16.0D0/27.0D0
COEFF(10,4)=-7296.0D0/157.0D0
COEFF(5,5)=9.0D0/2.0D0
COEFF(6,5)=1365.632D3/8352.1D1
COEFF(7,5)=-204.0D0/47.0D0
COEFF(8,5)=-456.0D0/47.0D0
COEFF(9,5)=16.0D0/459.0D0
COEFF(10,5)=2687.28D2/7379.0D0
COEFF(6,6)=-7820.8D1/2505.63D2
COEFF(7,6)=14.0D0/39.0D0
COEFF(8,6)=48.0D0/91.0D0
COEFF(9,6)=2907.2D1/1611.09D2
COEFF(10,6)=2472.0D0/2041.0D0
COEFF(7,7)=-4913.0D0/7820.8D1
COEFF(8,7)=1473.9D1/1368.64D2
COEFF(9,7)=-2023.0D0/7581.6D1
COEFF(10,7)=-3522.621D3/1074.3824D4
COEFF(8,8)=6.0D0/7.0D0
COEFF(9,8)=112.0D0/1239.3D1
COEFF(10,8)=132.0D0/157.0D0
COEFF(10,10)=-1239.3D1/4396.0D0
C
C A tilde values (see scheme)
C
COEFF(2,3)=2881.0D0/4032.0D1
COEFF(2,6)=1216.0D0/2961.0D0
COEFF(2,7)=-2624.0D0/4095.0D0
COEFF(2,8)=2413.7569D4/5748.2880D4
COEFF(2,9)=-4.0D0/21.0D0
COEFF(3,4)=4131.0D0/3920.0D0
COEFF(3,5)=-157.0D0/1260.0D0
C
C A - values (see scheme)
C
COEFF(1,1)=7.0D0/90.0D0
COEFF(1,4)=16.0D0/45.0D0
COEFF(1,5)=16.0D0/45.0D0
COEFF(1,7)=2.0D0/15.0D0
COEFF(1,8)=7.0D0/90.0D0
RETURN
END
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