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Index
SUBROUTINE RKV98 (M,COEFF,QG)
C
C*****************************************************************
C *
C This subroutine determines the coefficients for the embedding *
C formula RKV9(8) (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 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,H
C
C Initialize QG
C
QG=8.0D0
C
C Initialize H
C
H=DSQRT(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)=1.0D0/9.0D0
COEFF(4,1)=1.0D0/6.0D0
COEFF(5,1)=(2.0D0+2.0D0*H)/15.0D0
COEFF(6,1)=(6.0D0+1.0D0*H)/15.0D0
COEFF(7,1)=(6.0D0-1.0D0*H)/15.0D0
COEFF(8,1)=2.0D0/3.0D0
COEFF(9,1)=1.0D0/2.0D0
COEFF(10,1)=1.0D0/3.0D0
COEFF(11,1)=1.0D0/4.0D0
COEFF(12,1)=4.0D0/3.0D0
COEFF(13,1)=5.0D0/6.0D0
COEFF(14,1)=1.0D0
COEFF(15,1)=1.0D0/6.0D0
COEFF(16,1)=1.0D0
C
C b - values (see scheme)
C
COEFF(2,2)=1.0D0/12.0D0
COEFF(3,2)=1.0D0/27.0D0
COEFF(4,2)=1.0D0/24.0D0
COEFF(5,2)=(4.0D0+94.0D0*H)/375.0D0
COEFF(6,2)=(9.0D0-1.0D0*H)/150.0D0
COEFF(7,2)=(927.0D0-347.0D0*H)/1250.0D0
COEFF(8,2)=2.0D0/27.0D0
COEFF(9,2)=19.0D0/256.0D0
COEFF(10,2)=11.0D0/144.0D0
COEFF(11,2)=(5034.0D0-271.0D0*H)/6144.0D1
COEFF(12,2)=(5996.0D0-3794.0D0*H)/405.0D0
COEFF(13,2)=(3793.0D0+2168.0D0*H)/1036.80D2
COEFF(14,2)=-137.0D0/1296.0D0
COEFF(15,2)=(3361.7D1-2168.0D0*H)/5184.00D2
COEFF(16,2)=(-3648.7D1-3035.2D1*H)/2796.00D2
COEFF(3,3)=2.0D0/27.0D0
COEFF(4,4)=1.0D0/8.0D0
COEFF(5,4)=(-94.0D0-84.0D0*H)/125.0D0
COEFF(5,5)=(328.0D0+208.0D0*H)/375.0D0
COEFF(6,5)=(312.0D0+32.0D0*H)/1425.0D0
COEFF(7,5)=(-1624.8D1+7328.0D0*H)/9375.0D0
COEFF(6,6)=(69.0D0+29.0D0*H)/570.0D0
COEFF(7,6)=(-489.0D0+179.0D0*H)/3750.0D0
COEFF(7,7)=(1426.8D1-5798.0D0*H)/9375.0D0
COEFF(8,7)=(16.0D0-1.0D0*H)/54.0D0
COEFF(9,7)=(118.0D0-23.0D0*H)/512.0D0
COEFF(10,7)=(266.0D0-1.0D0*H)/864.0D0
COEFF(12,7)=(-4342.0D0-338.0D0*H)/9.0D0
COEFF(13,7)=(4042.0D0+2263.0D0*H)/1382.4D1
COEFF(14,7)=(5642.0D0-337.0D0*H)/864.0D0
COEFF(15,7)=(-3846.0D0+31.0D0*H)/1382.4D1
COEFF(16,7)=(-2966.6D1-4499.0D0*H)/7456.0D0
COEFF(8,8)=(16.0D0+1.0D0*H)/54.0D0
COEFF(9,8)=(118.0D0+23.0D0*H)/512.0D0
COEFF(10,8)=(266.0D0+1.0D0*H)/864.0D0
COEFF(11,8)=(7859.0D0-1626.0D0*H)/1024.0D1
COEFF(12,8)=(1549.22D2-4045.8D1*H)/135.0D0
COEFF(13,8)=(-2312.78D2+4071.7D1*H)/6912.0D1
COEFF(14,8)=(5642.0D0+337.0D0*H)/864.0D0
COEFF(15,8)=(1553.38D2-5280.7D1*H)/3456.00D2
COEFF(16,8)=(2779.182D3-6159.73D2*H)/1864.00D2
COEFF(9,9)=-9.0D0/256.0D0
COEFF(10,9)=-1.0D0/16.0D0
COEFF(11,9)=(-2232.0D0+813.0D0*H)/2048.0D1
COEFF(12,9)=(-4176.0D0+3794.0D0*H)/45.0D0
COEFF(13,9)=(7947.0D0-2168.0D0*H)/1152.0D1
COEFF(14,9)=-299.0D0/48.0D0
COEFF(15,9)=(-1253.7D1+2168.0D0*H)/5760.0D1
COEFF(16,9)=(-9432.9D1+9105.6D1*H)/9320.0D1
COEFF(10,10)=-8.0D0/27.0D0
COEFF(11,10)=(-594.0D0+271.0D0*H)/960.0D0
COEFF(12,10)=(-3408.64D2+2428.16D2*H)/405.0D0
COEFF(13,10)=(1048.0D0-542.0D0*H)/405.0D0
COEFF(14,10)=184.0D0/81.0D0
COEFF(15,10)=(92.0D0+542.0D0*H)/2025.0D0
COEFF(16,10)=(-2321.92D2+1214.08D2*H)/1747.5D1
COEFF(11,11)=(657.0D0-813.0D0*H)/5120.0D0
COEFF(12,11)=(2630.4D1-1517.6D1*H)/45.0D0
COEFF(13,11)=(-1383.0D0+542.0D0*H)/720.0D0
COEFF(14,11)=-44.0D0/9.0D0
COEFF(15,11)=(-1797.0D0-542.0D0*H)/3600.0D0
COEFF(16,11)=(1012.26D2-2276.4D1*H)/5825.0D0
COEFF(12,12)=-2662.4D1/81.0D0
COEFF(13,12)=2624.0D0/1053.0D0
COEFF(14,12)=-5120.0D0/1053.0D0
COEFF(15,12)=320.0D0/567.0D0
COEFF(16,12)=-1699.84D2/9087.0D0
COEFF(13,13)=3.0D0/1664.0D0
COEFF(14,13)=-11.0D0/468.0D0
COEFF(15,13)=-1.0D0/1920.0D0
COEFF(16,13)=-87.0D0/3029.0D1
COEFF(14,14)=16.0D0/9.0D0
COEFF(15,14)=4.0D0/105.0D0
COEFF(16,14)=492.0D0/1165.0D0
COEFF(16,16)=1260.0D0/233.0D0
C
C A tilde values (see scheme)
C
COEFF(2,3)=23.0D0/525.0D0
COEFF(2,10)=171.0D0/1400.0D0
COEFF(2,11)=86.0D0/525.0D0
COEFF(2,12)=93.0D0/280.0D0
COEFF(2,13)=-2048.0D0/6825.0D0
COEFF(2,14)=-3.0D0/1820.0D1
COEFF(2,15)=39.0D0/175.0D0
COEFF(3,4)=9.0D0/25.0D0
COEFF(3,5)=233.0D0/4200.0D0
C
C A - values (see scheme)
C
COEFF(1,1)=103.0D0/1680.0D0
COEFF(1,8)=-27.0D0/140.0D0
COEFF(1,9)=76.0D0/105.0D0
COEFF(1,10)=-201.0D0/280.0D0
COEFF(1,11)=1024.0D0/1365.0D0
COEFF(1,12)=3.0D0/7280.0D0
COEFF(1,13)=12.0D0/35.0D0
COEFF(1,14)=9.0D0/280.0D0
\hbox{\JDhspace\verb`
RETURN
END
Begin of file
Contents
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