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SUBROUTINE RKV65A (M,COEFF,QG)
C
C*****************************************************************
C *
C This subroutine determines the coefficients for the embedding *
C formula RKV6(5)9A (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 LOCAL VARIABLES: *
C ================ *
C H : DOUBLE PRECISION auxiliary variable *
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,H
C
C Initialize QG
C
QG=5.0D0
C
C Initialize H
C
H=DSQRT(10.0D0)
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)=4.0D0/9.0D0-4.0D0/45.0D0*H
COEFF(4,1)=2.0D0/3.0D0-2.0D0/15.0D0*H
COEFF(5,1)=9.0D0/16.0D0
COEFF(6,1)=1.0D0/2.0D0
COEFF(7,1)=9.0D0/10.0D0
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)=(-268.0D0+92.0D0*H)/405.0D0
COEFF(4,2)=1.0D0/6.0D0-1.0D0/30.0D0*H
COEFF(5,2)=11.547D3/32.768D3+405.0D0/16.384D3*H
COEFF(6,2)=1.9662371D7/5.1149376D7+441.281D3/1.2787344D7*H
COEFF(7,2)=-15.4207593D7/36.9412160D7-
+ 182.9424339D7/1154.4130000D7*H
COEFF(8,2)=7059.4945601D7/2140.6013856D7+
+ 2147.3424323D7/2140.6013856D7*H
COEFF(9,2)=31.0D0/324.0D0-37.0D0/4860.0D0*H
COEFF(3,3)=(448.0D0-128.0D0*H)/405.0D0
COEFF(4,4)=1.0D0/2.0D0-1.0D0/10.0D0*H
COEFF(5,4)=-18.225D3/32.768D3-5103.0D0/16.384D3*H
COEFF(6,4)=-3.786045D6/5.683264D6-2.52663D5/7.10408D5*H
COEFF(7,4)=265.9895739D7/184.7060800D7+
+ 65.3855409D7/115.4413000D7*H
COEFF(8,4)=-79.4525145D7/8.8090592D7-
+ 24.9156075D7/8.8090592D7*H
COEFF(5,5)=12.555D3/16.384D3+2349.0D0/8192.0D0*H
COEFF(6,5)=157.0556745D7/182.1486112D7+
+ 29.0041461D7/91.0743056D7*H
COEFF(7,5)=-34949.2176711D7/59198.2986400D7-
+ 35978.4638379D7/147995.7466000D7*H
COEFF(8,5)=86629.0968775D7/25409.7312624D7+
+ 25699.8959765D7/25409.731224D7*H
COEFF(9,5)=(37.435D3-3235.0D0*H)/69.228D3
COEFF(6,6)=(-4.1227072D7+1.374464D6*H)/51.2292969D7
COEFF(7,6)=15392.0585664D7/9249.7341625D7+
+ 31106.6673408D7/46248.6708125D7*H
COEFF(8,6)=(-1596419.6472448D7-503942.9245312D7*H)/
+ 128636.7645159D7
COEFF(9,6)=-1.245184D6/1.090341D6+9.699328D6/1.6355115D7*H
COEFF(7,7)=-1944.0D0/1625.0D0-6804.0D0/8125.0D0*H
COEFF(8,7)=(17.017D3+5075.0D0*H)/1116.0D0
COEFF(9,7)=71.0D0/54.0D0-74.0D0/135.0D0*H
COEFF(8,8)=(42.875D3+16.625D3*H)/90.396D3
COEFF(9,8)=625.0D0/486.0D0-250.0D0/729.0D0*H
COEFF(9,9)=-23.0D0/21.0D0+37.0D0/105.0D0*H
C
C A tilde values (see scheme)
C
COEFF(2,3)=31.0D0/324.0D0-37.0D0/4860.0D0*H
COEFF(2,6)=(37.435D3-3235.0D0*H)/69.228D3
COEFF(2,7)=-1.245184D6/1.090341D6+9.699328D6/1.6355115D7*H
COEFF(2,8)=71.0D0/54.0D0-74.0D0/135.0D0*H
COEFF(2,9)=625.0D0/486.0D0-250.0D0/729.0D0*H
COEFF(3,4)=-23.0D0/21.0D0+37.0D0/105.0D0*H
C
C A - values (see scheme)
C
COEFF(1,1)=5.0D0/54.0D0-2.0D0/135.0D0*H
COEFF(1,4)=(2390.0D0+2290.0D0*H)/17.307D3
COEFF(1,5)=40.960D3/121.149D3+262.144D3/605.745D3*H
COEFF(1,6)=2.0D0/27.0D0-64.0D0/135.0D0*H
COEFF(1,8)=150.029D3/443.709D3-236.267D3/2.218545D6*H
COEFF(1,9)=2411.0D0/126.774D3+1921.0D0/63.387D3*H
RETURN
END
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