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subbim.f
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C -----------------------------------------------------------------------------------
C THIS MODULE IS PART OF THE CODE BIM.
C THE CODE BIM NUMERICALLY SOLVES (STIFF) DIFFERENTIAL ODE
C PROBLEMS.
C
C Copyright (C)2002-2007
C
C Authors: CECILIA MAGHERINI (cecilia.magherini@ing.unipi.it)
C LUIGI BRUGNANO (brugnano@math.unifi.it)
C
C
C This program is free software; you can redistribute it and/or
C modify it under the terms of the GNU General Public License
C as published by the Free Software Foundation; either version 2
C of the License, or (at your option) any later version.
C
C This program is distributed in the hope that it will be useful,
C but WITHOUT ANY WARRANTY; without even the implied warranty of
C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
C GNU General Public License for more details.
C
C Licensed under The GNU General Public License, Version 2 or later.
C http://www.gnu.org/licenses/info/GPLv2orLater.html
C
C You should have received a copy of the GNU General Public License
C along with this program; if not, write to the Free Software
C Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301,
C USA.
C -----------------------------------------------------------------------------------
ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
c c
c In case the ISNAN function is not supported. c
c c
ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
c logical function isnan(A)
c implicit none
c double precision A, B
c logical X
c B = A
c X = ( A .EQ. B )
c isnan = (.NOT.X)
c return
c end
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C
C BLENDSTEP
C
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
subroutine blendstep4(m,y0,f0,Y,F,h,theta,ipvt,Z,
& ldlu,mljac,mujac,ijob)
c
c Blended iteration for the 4th order method
c
implicit none
include 'param.dat'
integer k
parameter (k=3)
c Input parameters
integer m,ipvt(m),ldlu,mljac,mujac,ijob
double precision y0(m),f0(m),theta(ldlu,m),h
c I/O parameters
double precision Y(m,k),F(m,k)
c Output parameters
double precision Z(m,k)
c Local variables
integer i,j
C ---------------------------------------------------------------------------------------
C 4th order BIM
C ---------------------------------------------------------------------------------------
double precision DA4_1_1,DA4_1_2,DA4_1_3,DA4_1_4,
& DA4_2_1,DA4_2_2,DA4_2_3,DA4_2_4,
& DA4_3_1,DA4_3_2,DA4_3_3,DA4_3_4,
& DB4_1_1,DB4_1_2,DB4_1_3,DB4_1_4,
& DB4_2_1,DB4_2_2,DB4_2_3,DB4_2_4,
& DB4_3_1,DB4_3_2,DB4_3_3,DB4_3_4,
& A24_1_1,A24_1_2,A24_1_3,A24_1_4,
& A24_2_1,A24_2_2,A24_2_3,A24_2_4,
& A24_3_1,A24_3_2,A24_3_3,A24_3_4,
& B24_1_1,B24_2_1,B24_3_1
parameter(
& DA4_1_1=-102133D0/405000D0,
& DA4_1_2=98743D0/180000D0,
& DA4_1_3=-7387D0/22500D0,
& DA4_1_4=+51709D0/1620000D0,
& DA4_2_1=-1D0-140353D0/810000D0,
& DA4_2_2=+7387D0/9000D0,
& DA4_2_3=10613D0/18000D0,
& DA4_2_4=-96031D0/405000D0,
& DA4_3_1=-22613D0/30000D0,
& DA4_3_2=-22161D0/20000D0,
& DA4_3_3=+22161D0/10000D0,
& DA4_3_4=-21257D0/60000D0,
& A24_1_1=-302867D0/405000D0,
& A24_1_2= 81257D0/180000D0,
& A24_1_3= 7387D0/22500D0,
& A24_1_4=-51709D0/1620000D0,
& A24_2_1= 140353D0/810000D0,
& A24_2_2=-7387D0/9000D0,
& A24_2_3= 7387D0/18000D0,
& A24_2_4= 96031D0/405000D0,
& A24_3_1=-7387D0/30000D0,
& A24_3_2= 22161D0/20000D0,
& A24_3_3=-22161D0/10000D0,
& A24_3_4= 81257D0/60000D0,
& DB4_1_1= 919D0/13500D0,
& DB4_1_2= 4589D0/30000D0,
& DB4_1_3=-37D0/120D0,
& DB4_1_4= 3D0/40D0,
& DB4_2_1= 115387D0/270000D0,
& DB4_2_2= 17D0/15D0,
& DB4_2_3=-6161D0/30000D0,
& DB4_2_4=-1D0/15D0,
& DB4_3_1= 3D0/8D0,
& DB4_3_2= 9D0/8D0,
& DB4_3_3= 9D0/8D0,
& DB4_3_4=-3637D0/10000D0,
& B24_1_1=7387D0/27000D0,
& B24_2_1=-7387D0/270000D0,
& B24_3_1=0D0)
C ---------------------------------------------------------------------------------------
c Z=[y0 Y]*(DA)'
do i=1,m
Z(i,1)=y0(i)* DA4_1_1+Y(i,1)*DA4_1_2+Y(i,2)*DA4_1_3+
& Y(i,3)*DA4_1_4
Z(i,2)=y0(i)* DA4_2_1+Y(i,1)*DA4_2_2+Y(i,2)*DA4_2_3+
& Y(i,3)*DA4_2_4
Z(i,3)=y0(i)* DA4_3_1+Y(i,1)*DA4_3_2+Y(i,2)*DA4_3_3+
& Y(i,3)*DA4_3_4
end do
c Z=Z-h*[f0 F]*(dB)'
do i=1,m
Z(i,1) = Z(i,1)-
& h*(f0(i)* DB4_1_1+F(i,1)*DB4_1_2+F(i,2)*DB4_1_3+
& F(i,3)*DB4_1_4)
Z(i,2) = Z(i,2)-
& h*(f0(i)* DB4_2_1+F(i,1)*DB4_2_2+F(i,2)*DB4_2_3+
& F(i,3)*DB4_2_4)
Z(i,3) = Z(i,3)-
& h*(f0(i)* DB4_3_1+F(i,1)*DB4_3_2+F(i,2)*DB4_3_3+
& F(i,3)*DB4_3_4)
end do
c theta*Z=Z
call sollu(m,theta,ldlu,Z(1,1),mljac,mujac,ipvt,ijob)
call sollu(m,theta,ldlu,Z(1,2),mljac,mujac,ipvt,ijob)
call sollu(m,theta,ldlu,Z(1,3),mljac,mujac,ipvt,ijob)
c Z=Z+[y0 Y]*(A2)'
do i=1,m
Z(i,1)=Z(i,1)+
& y0(i)* A24_1_1+Y(i,1)*A24_1_2+Y(i,2)*A24_1_3+
& Y(i,3)* A24_1_4
Z(i,2)=Z(i,2)+
& y0(i)* A24_2_1+Y(i,1)*A24_2_2+Y(i,2)*A24_2_3+
& Y(i,3)* A24_2_4
Z(i,3)=Z(i,3)+
& y0(i)* A24_3_1+Y(i,1)*A24_3_2+Y(i,2)*A24_3_3+
& Y(i,3)* A24_3_4
end do
c Z=Z-h*[f0 F]*(B2)'
do i=1,m
Z(i,1)=Z(i,1)-h*(f0(i)*B24_1_1 + F(i,1)*gamma4)
Z(i,2)=Z(i,2)-h*(f0(i)*B24_2_1 + F(i,2)*gamma4)
Z(i,3)=Z(i,3)-h*(f0(i)*B24_3_1 + F(i,3)*gamma4)
end do
c theta*Z=Z
call sollu(m,theta,ldlu,Z(1,1),mljac,mujac,ipvt,ijob)
call sollu(m,theta,ldlu,Z(1,2),mljac,mujac,ipvt,ijob)
call sollu(m,theta,ldlu,Z(1,3),mljac,mujac,ipvt,ijob)
c
c Y = Y-Z
c
do j=1,k
do i=1,m
Y(i,j) = Y(i,j) - Z(i,j)
end do
end do
return
end
C -------------------------------------------------------------------
subroutine blendstep6(m,y0,f0,Y,F,h,theta,ipvt,Z,
& ldlu,mljac,mujac,ijob)
c
c Blended iteration for the 6th order method
c
implicit none
include 'param.dat'
integer k
parameter (k=4)
c Input parameters
integer m,ipvt(m),ldlu,mljac,mujac,ijob
double precision y0(m),f0(m),theta(ldlu,m),h
c I/O parameters
double precision Y(m,k),F(m,k)
c Output parameters
double precision Z(m,k)
c Local variables
integer i,j
C ---------------------------------------------------------------------------------------
C 6th order BIM
C ---------------------------------------------------------------------------------------
double precision DA6_1_1,DA6_1_2,DA6_1_3,DA6_1_4,DA6_1_5,
& DA6_2_1,DA6_2_2,DA6_2_3,DA6_2_4,DA6_2_5,
& DA6_3_1,DA6_3_2,DA6_3_3,DA6_3_4,DA6_3_5,
& DA6_4_1,DA6_4_2,DA6_4_3,DA6_4_4,DA6_4_5,
& DB6_1_1,DB6_1_2,DB6_1_3,DB6_1_4,DB6_1_5,
& DB6_2_1,DB6_2_2,DB6_2_3,DB6_2_4,DB6_2_5,
& DB6_3_1,DB6_3_2,DB6_3_3,DB6_3_4,DB6_3_5,
& DB6_4_1,DB6_4_2,DB6_4_3,DB6_4_4,DB6_4_5,
& A26_1_1,A26_1_2,A26_1_3,A26_1_4,A26_1_5,
& A26_2_1,A26_2_2,A26_2_3,A26_2_4,A26_2_5,
& A26_3_1,A26_3_2,A26_3_3,A26_3_4,A26_3_5,
& A26_4_1,A26_4_2,A26_4_3,A26_4_4,A26_4_5,
& B26_1_1,B26_2_1,B26_3_1,B26_4_1
parameter(
& DA6_1_1=-1171629D0/5120000D0,
& DA6_1_2=607997D0/960000D0,
& DA6_1_3=-597981D0/1280000D0,
& DA6_1_4=+4241D0/64000D0,
& DA6_1_5=-55133D0/15360000D0,
& DA6_2_1=-307277D0/320000D0,
& DA6_2_2=+4241D0/12000D0,
& DA6_2_3=1D0+12723D0/80000D0,
& DA6_2_4=-12723D0/20000D0,
& DA6_2_5=+80579D0/960000D0,
& DA6_3_1=-1D0-733693D0/5120000D0,
& DA6_3_2=-4241D0/320000 D0,
& DA6_3_3=+1234131D0/1280000D0,
& DA6_3_4=137637D0/320000D0,
& DA6_3_5=-1217167D0/5120000D0,
& DA6_4_1=-24241D0/20000D0,
& DA6_4_2=+4241D0/3750D0,
& DA6_4_3=-12723D0/5000D0,
& DA6_4_4=+4241D0/1250D0,
& DA6_4_5=-1841D0/2400D0,
& A26_1_1=-3948371D0/5120000D0,
& A26_1_2=352003D0/960000D0,
& A26_1_3=597981D0/1280000D0,
& A26_1_4=-4241D0/64000D0,
& A26_1_5=55133D0/15360000D0,
& A26_2_1=-12723D0/320000D0,
& A26_2_2=-4241D0/12000D0,
& A26_2_3=-12723D0/80000D0,
& A26_2_4=12723D0/20000D0,
& A26_2_5=-80579D0/960000D0,
& A26_3_1=733693D0/5120000D0,
& A26_3_2=4241D0/320000 D0,
& A26_3_3=-1234131D0/1280000D0,
& A26_3_4= 182363D0/320000D0,
& A26_3_5= 1217167D0/5120000D0,
& A26_4_1= 4241D0/20000D0,
& A26_4_2=-4241D0/3750D0,
& A26_4_3= 12723D0/5000D0,
& A26_4_4=-4241D0/1250D0,
& A26_4_5= 4241D0/2400D0,
& DB6_1_1=60311D0/11520000D0,
& DB6_1_2=7853D0/22500D0,
& DB6_1_3=-49D0/60D0,
& DB6_1_4=161D0/360D0,
& DB6_1_5=-73D0/720D0,
& DB6_2_1=257831D0/720000D0,
& DB6_2_2=46D0/45D0,
& DB6_2_3=-241D0/5000D0,
& DB6_2_4=-14D0/45D0,
& DB6_2_5=7D0/90D0,
& DB6_3_1=1850413D0/3840000D0,
& DB6_3_2=133D0/120D0,
& DB6_3_3=23D0/20D0,
& DB6_3_4=-1837D0/3750D0,
& DB6_3_5=1D0/240D0,
& DB6_4_1=14D0/45D0,
& DB6_4_2=64D0/45D0,
& DB6_4_3=8D0/15D0,
& DB6_4_4=64D0/45D0,
& DB6_4_5=-24169D0/45000D0,
& B26_1_1=343521D0/1280000D0,
& B26_2_1=4241D0/80000D0,
& B26_3_1=-131471D0/1280000D0,
& B26_4_1=0D0)
C ---------------------------------------------------------------------------------------
c Z=[y0 Y]*(DA)'
do i=1,m
Z(i,1)=y0(i)* DA6_1_1+Y(i,1)*DA6_1_2+Y(i,2)*DA6_1_3+
& Y(i,3)*DA6_1_4+Y(i,4)*DA6_1_5
Z(i,2)=y0(i)* DA6_2_1+Y(i,1)*DA6_2_2+Y(i,2)*DA6_2_3+
& Y(i,3)*DA6_2_4+Y(i,4)*DA6_2_5
Z(i,3)=y0(i)* DA6_3_1+Y(i,1)*DA6_3_2+Y(i,2)*DA6_3_3+
& Y(i,3)*DA6_3_4+Y(i,4)*DA6_3_5
Z(i,4)=y0(i)* DA6_4_1+Y(i,1)*DA6_4_2+Y(i,2)*DA6_4_3+
& Y(i,3)*DA6_4_4+Y(i,4)*DA6_4_5
end do
c Z=Z-h*[f0 F]*(dB)'
do i=1,m
Z(i,1) = Z(i,1)-
& h*(f0(i)* DB6_1_1+F(i,1)*DB6_1_2+F(i,2)*DB6_1_3+
& F(i,3)*DB6_1_4+F(i,4)*DB6_1_5)
Z(i,2) = Z(i,2)-
& h*(f0(i)* DB6_2_1+F(i,1)*DB6_2_2+F(i,2)*DB6_2_3+
& F(i,3)*DB6_2_4+F(i,4)*DB6_2_5)
Z(i,3) = Z(i,3)-
& h*(f0(i)* DB6_3_1+F(i,1)*DB6_3_2+F(i,2)*DB6_3_3+
& F(i,3)*DB6_3_4+F(i,4)*DB6_3_5)
Z(i,4) = Z(i,4)-
& h*(f0(i)* DB6_4_1+F(i,1)*DB6_4_2+F(i,2)*DB6_4_3+
& F(i,3)*DB6_4_4+F(i,4)*DB6_4_5)
end do
c theta*Z=Z
call sollu(m,theta,ldlu,Z(1,1),mljac,mujac,ipvt,ijob)
call sollu(m,theta,ldlu,Z(1,2),mljac,mujac,ipvt,ijob)
call sollu(m,theta,ldlu,Z(1,3),mljac,mujac,ipvt,ijob)
call sollu(m,theta,ldlu,Z(1,4),mljac,mujac,ipvt,ijob)
c Z=Z+[y0 Y]*(A2)'
do i=1,m
Z(i,1)=Z(i,1)+
& y0(i)* A26_1_1+Y(i,1)*A26_1_2+Y(i,2)*A26_1_3+
& Y(i,3)* A26_1_4+Y(i,4)*A26_1_5
Z(i,2)=Z(i,2)+
& y0(i)* A26_2_1+Y(i,1)*A26_2_2+Y(i,2)*A26_2_3+
& Y(i,3)* A26_2_4+Y(i,4)*A26_2_5
Z(i,3)=Z(i,3)+
& y0(i)* A26_3_1+Y(i,1)*A26_3_2+Y(i,2)*A26_3_3+
& Y(i,3)* A26_3_4+Y(i,4)*A26_3_5
Z(i,4)=Z(i,4)+
& y0(i)* A26_4_1+Y(i,1)*A26_4_2+Y(i,2)*A26_4_3+
& Y(i,3)* A26_4_4+Y(i,4)*A26_4_5
end do
c Z=Z-h*[f0 F]*(B2)'
do i=1,m
Z(i,1)=Z(i,1)-h*(f0(i)*B26_1_1 + F(i,1)*gamma6)
Z(i,2)=Z(i,2)-h*(f0(i)*B26_2_1 + F(i,2)*gamma6)
Z(i,3)=Z(i,3)-h*(f0(i)*B26_3_1 + F(i,3)*gamma6)
Z(i,4)=Z(i,4)-h*(f0(i)*B26_4_1 + F(i,4)*gamma6)
end do
c theta*Z=Z
call sollu(m,theta,ldlu,Z(1,1),mljac,mujac,ipvt,ijob)
call sollu(m,theta,ldlu,Z(1,2),mljac,mujac,ipvt,ijob)
call sollu(m,theta,ldlu,Z(1,3),mljac,mujac,ipvt,ijob)
call sollu(m,theta,ldlu,Z(1,4),mljac,mujac,ipvt,ijob)
c
c Y = Y-Z
c
do j=1,k
do i=1,m
Y(i,j) = Y(i,j) - Z(i,j)
end do
end do
return
end
C -------------------------------------------------------------------
subroutine blendstep8(m,y0,f0,Y,F,h,theta,ipvt,Z,
& ldlu,mljac,mujac,ijob)
c
c Blended iteration for the 8th order method
c
implicit none
include 'param.dat'
integer k
parameter (k=6)
c Input parameters
integer m,ipvt(m),ldlu,mljac,mujac,ijob
double precision y0(m),f0(m),theta(ldlu,m),h
c I/O parameters
double precision Y(m,k),F(m,k)
c Output parameters
double precision Z(m,k)
c Local variables
integer i,j
C ---------------------------------------------------------------------------------------
C 8th order BIM
C ---------------------------------------------------------------------------------------
double precision
& DA8_1_1,DA8_1_2,DA8_1_3,DA8_1_4,DA8_1_5,DA8_1_6,DA8_1_7,
& DA8_2_1,DA8_2_2,DA8_2_3,DA8_2_4,DA8_2_5,DA8_2_6,DA8_2_7,
& DA8_3_1,DA8_3_2,DA8_3_3,DA8_3_4,DA8_3_5,DA8_3_6,DA8_3_7,
& DA8_4_1,DA8_4_2,DA8_4_3,DA8_4_4,DA8_4_5,DA8_4_6,DA8_4_7,
& DA8_5_1,DA8_5_2,DA8_5_3,DA8_5_4,DA8_5_5,DA8_5_6,DA8_5_7,
& DA8_6_1,DA8_6_2,DA8_6_3,DA8_6_4,DA8_6_5,DA8_6_6,DA8_6_7,
& DB8_1_1,DB8_1_2,DB8_1_3,DB8_1_4,DB8_1_5,DB8_1_6,DB8_1_7,
& DB8_2_1,DB8_2_2,DB8_2_3,DB8_2_4,DB8_2_5,DB8_2_6,DB8_2_7,
& DB8_3_1,DB8_3_2,DB8_3_3,DB8_3_4,DB8_3_5,DB8_3_6,DB8_3_7,
& DB8_4_1,DB8_4_2,DB8_4_3,DB8_4_4,DB8_4_5,DB8_4_6,DB8_4_7,
& DB8_5_1,DB8_5_2,DB8_5_3,DB8_5_4,DB8_5_5,DB8_5_6,DB8_5_7,
& DB8_6_1,DB8_6_2,DB8_6_3,DB8_6_4,DB8_6_5,DB8_6_6,DB8_6_7,
& A28_1_1,A28_1_2,A28_1_3,A28_1_4,A28_1_5,A28_1_6,A28_1_7,
& A28_2_1,A28_2_2,A28_2_3,A28_2_4,A28_2_5,A28_2_6,A28_2_7,
& A28_3_1,A28_3_2,A28_3_3,A28_3_4,A28_3_5,A28_3_6,A28_3_7,
& A28_4_1,A28_4_2,A28_4_3,A28_4_4,A28_4_5,A28_4_6,A28_4_7,
& A28_5_1,A28_5_2,A28_5_3,A28_5_4,A28_5_5,A28_5_6,A28_5_7,
& A28_6_1,A28_6_2,A28_6_3,A28_6_4,A28_6_5,A28_6_6,A28_6_7,
& B28_1_1,B28_2_1,B28_3_1,B28_4_1,B28_5_1,B28_6_1
parameter(
& DA8_1_1 = -24312887D0/62208000D0,
& DA8_1_2 = 9595787D0/12960000D0,
& DA8_1_3 = - 680419D0/2073600D0,
& DA8_1_4 = - 263717D0/2332800D0,
& DA8_1_5 = + 578429D0/4147200D0,
& DA8_1_6 = - 147157D0/2592000D0,
& DA8_1_7 = + 4150993D0/466560000D0,
& DA8_2_1 = -1D0 - 394847D0/972000D0,
& DA8_2_2 = +496837D0/405000D0,
& DA8_2_3 = 165733D0/648000D0,
& DA8_2_4 = +24769D0/364500D0,
& DA8_2_5 = -71393D0/324000D0,
& DA8_2_6 = +1457D0/16200D0,
& DA8_2_7 = -403589D0/29160000D0,
& DA8_3_1 = -1D0 -33511D0/768000D0,
& DA8_3_2 = +4371D0/160000D0,
& DA8_3_3 = +48081D0/128000D0,
& DA8_3_4 = 1D0 +1457D0/9600D0,
& DA8_3_5 = -161727D0/256000D0,
& DA8_3_6 = +4371D0/32000D0,
& DA8_3_7 = -10199D0/640000D0,
& DA8_4_1 = -388381D0/486000D0,
& DA8_4_2 = -85963D0/202500D0,
& DA8_4_3 = +2914D0/10125D0,
& DA8_4_4 = +71393D0/182250D0,
& DA8_4_5 = 145973D0/162000D0,
& DA8_4_6 = -16027D0/40500D0,
& DA8_4_7 = +141329D0/3645000D0,
& DA8_5_1 = -1D0 -2073311D0/62208000D0,
& DA8_5_2 = -106361D0/2592000D0,
& DA8_5_3 = +893141D0/2073600D0,
& DA8_5_4 = -2466701D0/2332800D0,
& DA8_5_5 = +7187381D0/4147200D0,
& DA8_5_6 = 241859D0/2592000D0,
& DA8_5_7 = -11695339D0/93312000D0,
& DA8_6_1 = -1D0 -1457D0/12000D0,
& DA8_6_2 = +4371D0/5000D0,
& DA8_6_3 = -4371D0/1600D0,
& DA8_6_4 = +1457D0/300D0,
& DA8_6_5 = -4371D0/800D0,
& DA8_6_6 = +4371D0/1000D0,
& DA8_6_7 = -31393D0/40000D0,
& A28_1_1 = -37895113D0/62208000D0,
& A28_1_2 = 3364213D0/12960000D0,
& A28_1_3 = 680419D0/2073600D0,
& A28_1_4 = 263717D0/2332800D0,
& A28_1_5 = -578429D0/4147200D0,
& A28_1_6 = 147157D0/2592000D0,
& A28_1_7 = -4150993D0/466560000D0,
& A28_2_1 = 394847D0/972000D0,
& A28_2_2 = -496837D0/405000D0,
& A28_2_3 = 482267D0/648000D0,
& A28_2_4 = -24769D0/364500D0,
& A28_2_5 = 71393D0/324000D0,
& A28_2_6 = -1457D0/16200D0,
& A28_2_7 = 403589D0/29160000D0,
& A28_3_1 = 33511D0/768000D0,
& A28_3_2 = -4371D0/160000D0,
& A28_3_3 = -48081D0/128000D0,
& A28_3_4 = -1457D0/9600D0,
& A28_3_5 = 161727D0/256000D0,
& A28_3_6 = -4371D0/32000D0,
& A28_3_7 = 10199D0/640000D0,
& A28_4_1 = -97619D0/486000D0,
& A28_4_2 = 85963D0/202500D0,
& A28_4_3 = -2914D0/10125D0,
& A28_4_4 = -71393D0/182250D0,
& A28_4_5 = 16027D0/162000D0,
& A28_4_6 = 16027D0/40500D0,
& A28_4_7 = -141329D0/3645000D0,
& A28_5_1 = 2073311D0/62208000D0,
& A28_5_2 = 106361D0/2592000D0,
& A28_5_3 = -893141D0/2073600D0,
& A28_5_4 = 2466701D0/2332800D0,
& A28_5_5 = -7187381D0/4147200D0,
& A28_5_6 = 2350141D0/2592000D0,
& A28_5_7 = 11695339D0/93312000D0,
& A28_6_1 = 1457D0/12000D0,
& A28_6_2 = -4371D0/5000D0,
& A28_6_3 = 4371D0/1600D0,
& A28_6_4 = -1457D0/300D0,
& A28_6_5 = 4371D0/800D0,
& A28_6_6 = -4371D0/1000D0,
& A28_6_7 = 71393D0/40000D0,
& DB8_1_1 = 87907D0/622080D0,
& DB8_1_2 = 3587D0/18000D0,
& DB8_1_3 = -1141D0/2880D0,
& DB8_1_4 = 67D0/540D0,
& DB8_1_5 = 109D0/2880D0,
& DB8_1_6 = -2D0/45D0,
& DB8_1_7 = 91D0/8640D0,
& DB8_2_1 = 203071D0/425250D0,
& DB8_2_2 = 2158D0/1575D0,
& DB8_2_3 = -52291D0/126000D0,
& DB8_2_4 = -52D0/945D0,
& DB8_2_5 = 23D0/252D0,
& DB8_2_6 = -82D0/1575D0,
& DB8_2_7 = 199D0/18900D0,
& DB8_3_1 = 19177D0/64000D0,
& DB8_3_2 = 81D0/50D0,
& DB8_3_3 = 27D0/320D0,
& DB8_3_4 = 1643D0/2000D0,
& DB8_3_5 = -243D0/320D0,
& DB8_3_6 = 27D0/100D0,
& DB8_3_7 = -67D0/1600D0,
& DB8_4_1 = 716549D0/3402000D0,
& DB8_4_2 = 2368D0/1575D0,
& DB8_4_3 = 104D0/315D0,
& DB8_4_4 = 320D0/189D0,
& DB8_4_5 = -78191D0/126000D0,
& DB8_4_6 = 128D0/1575D0,
& DB8_4_7 = -64D0/4725D0,
& DB8_5_1 = 37053349D0/108864000D0,
& DB8_5_2 = 1739D0/1260D0,
& DB8_5_3 = 2713D0/4032D0,
& DB8_5_4 = 853D0/756D0,
& DB8_5_5 = 4463D0/4032D0,
& DB8_5_6 = -40391D0/126000D0,
& DB8_5_7 = -787D0/60480D0,
& DB8_6_1 = 41D0/140D0,
& DB8_6_2 = 54D0/35D0,
& DB8_6_3 = 27D0/140D0,
& DB8_6_4 = 68D0/35D0,
& DB8_6_5 = 27D0/140D0,
& DB8_6_6 = 54D0/35D0,
& DB8_6_7 = -6099D0/14000D0,
& B28_1_1 = 24769D0/124416D0,
& B28_2_1 = -18941D0/121500D0,
& B28_3_1 = -1457D0/64000D0,
& B28_4_1 = 42253D0/486000D0,
& B28_5_1 = -365707D0/15552000D0,
& B28_6_1 = 0D0)
C ---------------------------------------------------------------------------------------
c Z=[y0 Y]*(DA)'
do i=1,m
Z(i,1)=y0(i)* DA8_1_1+Y(i,1)*DA8_1_2+Y(i,2)*DA8_1_3+
& Y(i,3)*DA8_1_4+Y(i,4)*DA8_1_5+Y(i,5)*DA8_1_6+
& Y(i,6)*DA8_1_7
Z(i,2)=y0(i)* DA8_2_1+Y(i,1)*DA8_2_2+Y(i,2)*DA8_2_3+
& Y(i,3)*DA8_2_4+Y(i,4)*DA8_2_5+Y(i,5)*DA8_2_6+
& Y(i,6)*DA8_2_7
Z(i,3)=y0(i)* DA8_3_1+Y(i,1)*DA8_3_2+Y(i,2)*DA8_3_3+
& Y(i,3)*DA8_3_4+Y(i,4)*DA8_3_5+Y(i,5)*DA8_3_6+
& Y(i,6)*DA8_3_7
Z(i,4)=y0(i)* DA8_4_1+Y(i,1)*DA8_4_2+Y(i,2)*DA8_4_3+
& Y(i,3)*DA8_4_4+Y(i,4)*DA8_4_5+Y(i,5)*DA8_4_6+
& Y(i,6)*DA8_4_7
Z(i,5)=y0(i)* DA8_5_1+Y(i,1)*DA8_5_2+Y(i,2)*DA8_5_3+
& Y(i,3)*DA8_5_4+Y(i,4)*DA8_5_5+Y(i,5)*DA8_5_6+
& Y(i,6)*DA8_5_7
Z(i,6)=y0(i)* DA8_6_1+Y(i,1)*DA8_6_2+Y(i,2)*DA8_6_3+
& Y(i,3)*DA8_6_4+Y(i,4)*DA8_6_5+Y(i,5)*DA8_6_6+
& Y(i,6)*DA8_6_7
end do
c Z=Z-h*[f0 F]*(dB)'
do i=1,m
Z(i,1) = Z(i,1)-
& h*(f0(i)* DB8_1_1+F(i,1)*DB8_1_2+F(i,2)*DB8_1_3+
& F(i,3)*DB8_1_4+F(i,4)*DB8_1_5+F(i,5)*DB8_1_6+
& F(i,6)*DB8_1_7)
Z(i,2) = Z(i,2)-
& h*(f0(i)* DB8_2_1+F(i,1)*DB8_2_2+F(i,2)*DB8_2_3+
& F(i,3)*DB8_2_4+F(i,4)*DB8_2_5+F(i,5)*DB8_2_6+
& F(i,6)*DB8_2_7)
Z(i,3) = Z(i,3)-
& h*(f0(i)* DB8_3_1+F(i,1)*DB8_3_2+F(i,2)*DB8_3_3+
& F(i,3)*DB8_3_4+F(i,4)*DB8_3_5+F(i,5)*DB8_3_6+
& F(i,6)*DB8_3_7)
Z(i,4) = Z(i,4)-
& h*(f0(i)* DB8_4_1+F(i,1)*DB8_4_2+F(i,2)*DB8_4_3+
& F(i,3)*DB8_4_4+F(i,4)*DB8_4_5+F(i,5)*DB8_4_6+
& F(i,6)*DB8_4_7)
Z(i,5) = Z(i,5)-
& h*(f0(i)* DB8_5_1+F(i,1)*DB8_5_2+F(i,2)*DB8_5_3+
& F(i,3)*DB8_5_4+F(i,4)*DB8_5_5+F(i,5)*DB8_5_6+
& F(i,6)*DB8_5_7)
Z(i,6) = Z(i,6)-
& h*(f0(i)* DB8_6_1+F(i,1)*DB8_6_2+F(i,2)*DB8_6_3+
& F(i,3)*DB8_6_4+F(i,4)*DB8_6_5+F(i,5)*DB8_6_6+
& F(i,6)*DB8_6_7)
end do
c theta*Z=Z
call sollu(m,theta,ldlu,Z(1,1),mljac,mujac,ipvt,ijob)
call sollu(m,theta,ldlu,Z(1,2),mljac,mujac,ipvt,ijob)
call sollu(m,theta,ldlu,Z(1,3),mljac,mujac,ipvt,ijob)
call sollu(m,theta,ldlu,Z(1,4),mljac,mujac,ipvt,ijob)
call sollu(m,theta,ldlu,Z(1,5),mljac,mujac,ipvt,ijob)
call sollu(m,theta,ldlu,Z(1,6),mljac,mujac,ipvt,ijob)
c Z=Z+[y0 Y]*(A2)'
do i=1,m
Z(i,1)=Z(i,1)+
& y0(i)* A28_1_1+Y(i,1)*A28_1_2+Y(i,2)*A28_1_3+
& Y(i,3)* A28_1_4+Y(i,4)*A28_1_5+Y(i,5)*A28_1_6+
& Y(i,6)* A28_1_7
Z(i,2)=Z(i,2)+
& y0(i)* A28_2_1+Y(i,1)*A28_2_2+Y(i,2)*A28_2_3+
& Y(i,3)* A28_2_4+Y(i,4)*A28_2_5+Y(i,5)*A28_2_6+
& Y(i,6)* A28_2_7
Z(i,3)=Z(i,3)+
& y0(i)* A28_3_1+Y(i,1)*A28_3_2+Y(i,2)*A28_3_3+
& Y(i,3)* A28_3_4+Y(i,4)*A28_3_5+Y(i,5)*A28_3_6+
& Y(i,6)* A28_3_7
Z(i,4)=Z(i,4)+
& y0(i)* A28_4_1+Y(i,1)*A28_4_2+Y(i,2)*A28_4_3+
& Y(i,3)* A28_4_4+Y(i,4)*A28_4_5+Y(i,5)*A28_4_6+
& Y(i,6)* A28_4_7
Z(i,5)=Z(i,5)+
& y0(i)* A28_5_1+Y(i,1)*A28_5_2+Y(i,2)*A28_5_3+
& Y(i,3)* A28_5_4+Y(i,4)*A28_5_5+Y(i,5)*A28_5_6+
& Y(i,6)* A28_5_7
Z(i,6)=Z(i,6)+
& y0(i)* A28_6_1+Y(i,1)*A28_6_2+Y(i,2)*A28_6_3+
& Y(i,3)* A28_6_4+Y(i,4)*A28_6_5+Y(i,5)*A28_6_6+
& Y(i,6)* A28_6_7
end do
c Z=Z-h*[f0 F]*(B2)'
do i=1,m
Z(i,1)=Z(i,1)-h*(f0(i)*B28_1_1 + F(i,1)*gamma8)
Z(i,2)=Z(i,2)-h*(f0(i)*B28_2_1 + F(i,2)*gamma8)
Z(i,3)=Z(i,3)-h*(f0(i)*B28_3_1 + F(i,3)*gamma8)
Z(i,4)=Z(i,4)-h*(f0(i)*B28_4_1 + F(i,4)*gamma8)
Z(i,5)=Z(i,5)-h*(f0(i)*B28_5_1 + F(i,5)*gamma8)
Z(i,6)=Z(i,6)-h*(f0(i)*B28_6_1 + F(i,6)*gamma8)
end do
c theta*Z=Z
call sollu(m,theta,ldlu,Z(1,1),mljac,mujac,ipvt,ijob)
call sollu(m,theta,ldlu,Z(1,2),mljac,mujac,ipvt,ijob)
call sollu(m,theta,ldlu,Z(1,3),mljac,mujac,ipvt,ijob)
call sollu(m,theta,ldlu,Z(1,4),mljac,mujac,ipvt,ijob)
call sollu(m,theta,ldlu,Z(1,5),mljac,mujac,ipvt,ijob)
call sollu(m,theta,ldlu,Z(1,6),mljac,mujac,ipvt,ijob)
c
c Y = Y-Z
c
do j=1,k
do i=1,m
Y(i,j) = Y(i,j) - Z(i,j)
end do
end do
return
end
C -------------------------------------------------------------------
subroutine blendstep10(m,y0,f0,Y,F,h,theta,ipvt,Z,
& ldlu,mljac,mujac,ijob)
c
c Blended iteration for the 10th order method
c
implicit none
include 'param.dat'
integer k
parameter (k=8)
c Input parameters
integer m,ipvt(m),ldlu,mljac,mujac,ijob
double precision y0(m),f0(m),theta(ldlu,m),h
c I/O parameters
double precision Y(m,k),F(m,k)
c Output parameters
double precision Z(m,k)
c Local variables
integer i,j
C ---------------------------------------------------------------------------------------
C 10th order BIM
C ---------------------------------------------------------------------------------------
double precision
& DA10_1_1,DA10_1_2,DA10_1_3,DA10_1_4,DA10_1_5,DA10_1_6,DA10_1_7,
& DA10_1_8,DA10_1_9,
& DA10_2_1,DA10_2_2,DA10_2_3,DA10_2_4,DA10_2_5,DA10_2_6,DA10_2_7,
& DA10_2_8,DA10_2_9,
& DA10_3_1,DA10_3_2,DA10_3_3,DA10_3_4,DA10_3_5,DA10_3_6,DA10_3_7,
& DA10_3_8,DA10_3_9,
& DA10_4_1,DA10_4_2,DA10_4_3,DA10_4_4,DA10_4_5,DA10_4_6,DA10_4_7,
& DA10_4_8,DA10_4_9,
& DA10_5_1,DA10_5_2,DA10_5_3,DA10_5_4,DA10_5_5,DA10_5_6,DA10_5_7,
& DA10_5_8,DA10_5_9,
& DA10_6_1,DA10_6_2,DA10_6_3,DA10_6_4,DA10_6_5,DA10_6_6,DA10_6_7,
& DA10_6_8,DA10_6_9,
& DA10_7_1,DA10_7_2,DA10_7_3,DA10_7_4,DA10_7_5,DA10_7_6,DA10_7_7,
& DA10_7_8,DA10_7_9,
& DA10_8_1,DA10_8_2,DA10_8_3,DA10_8_4,DA10_8_5,DA10_8_6,DA10_8_7,
& DA10_8_8,DA10_8_9,
& DB10_1_1,DB10_1_2,DB10_1_3,DB10_1_4,DB10_1_5,DB10_1_6,DB10_1_7,
& DB10_1_8,DB10_1_9,
& DB10_2_1,DB10_2_2,DB10_2_3,DB10_2_4,DB10_2_5,DB10_2_6,DB10_2_7,
& DB10_2_8,DB10_2_9,
& DB10_3_1,DB10_3_2,DB10_3_3,DB10_3_4,DB10_3_5,DB10_3_6,DB10_3_7,
& DB10_3_8,DB10_3_9,
& DB10_4_1,DB10_4_2,DB10_4_3,DB10_4_4,DB10_4_5,DB10_4_6,DB10_4_7,
& DB10_4_8,DB10_4_9,
& DB10_5_1,DB10_5_2,DB10_5_3,DB10_5_4,DB10_5_5,DB10_5_6,DB10_5_7,
& DB10_5_8,DB10_5_9,
& DB10_6_1,DB10_6_2,DB10_6_3,DB10_6_4,DB10_6_5,DB10_6_6,DB10_6_7,
& DB10_6_8,DB10_6_9,
& DB10_7_1,DB10_7_2,DB10_7_3,DB10_7_4,DB10_7_5,DB10_7_6,DB10_7_7,
& DB10_7_8,DB10_7_9,
& DB10_8_1,DB10_8_2,DB10_8_3,DB10_8_4,DB10_8_5,DB10_8_6,DB10_8_7,
& DB10_8_8,DB10_8_9,
& A210_1_1,A210_1_2,A210_1_3,A210_1_4,A210_1_5,A210_1_6,A210_1_7,
& A210_1_8,A210_1_9,
& A210_2_1,A210_2_2,A210_2_3,A210_2_4,A210_2_5,A210_2_6,A210_2_7,
& A210_2_8,A210_2_9,
& A210_3_1,A210_3_2,A210_3_3,A210_3_4,A210_3_5,A210_3_6,A210_3_7,
& A210_3_8,A210_3_9,
& A210_4_1,A210_4_2,A210_4_3,A210_4_4,A210_4_5,A210_4_6,A210_4_7,
& A210_4_8,A210_4_9,
& A210_5_1,A210_5_2,A210_5_3,A210_5_4,A210_5_5,A210_5_6,A210_5_7,
& A210_5_8,A210_5_9,
& A210_6_1,A210_6_2,A210_6_3,A210_6_4,A210_6_5,A210_6_6,A210_6_7,
& A210_6_8,A210_6_9,
& A210_7_1,A210_7_2,A210_7_3,A210_7_4,A210_7_5,A210_7_6,A210_7_7,
& A210_7_8,A210_7_9,
& A210_8_1,A210_8_2,A210_8_3,A210_8_4,A210_8_5,A210_8_6,A210_8_7,
& A210_8_8,A210_8_9,
& B210_1_1,B210_2_1,B210_3_1,B210_4_1,B210_5_1,B210_6_1,B210_7_1,
& B210_8_1
parameter(
& DA10_1_1 = -1116185640857D0/1342177280000D0,
& DA10_1_2 = 1D0 +121395173141D0/146800640000D0,
& DA10_1_3 = -6468370013D0/3355443200D0,
& DA10_1_4 = +22440146897D0/12582912000D0,
& DA10_1_5 = -57418737523D0/40265318400D0,
& DA10_1_6 = +17489295313D0/20971520000D0,
& DA10_1_7 = -82495624981D0/251658240000D0,
& DA10_1_8 = +193947079D0/2516582400D0,
& DA10_1_9 = -15367501777D0/1879048192000D0,
& DA10_2_1 = -1D0 -359763461D0/1048576000D0,
& DA10_2_2 = +133859921D0/114688000D0,
& DA10_2_3 = -21140373D0/327680000D0,
& DA10_2_4 = +15150619D0/16384000D0,
& DA10_2_5 = -67553873D0/52428800D0,
& DA10_2_6 = +44952727D0/49152000D0,
& DA10_2_7 = -26201627D0/65536000D0,
& DA10_2_8 = +8246437D0/81920000D0,
& DA10_2_9 = -246865651D0/22020096000D0,
& DA10_3_1 = -552495440623D0/805306368000D0,
& DA10_3_2 = -28197945999D0/29360128000D0,
& DA10_3_3 = +32441533071D0/16777216000D0,
& DA10_3_4 = -51906383051D0/62914560000D0,
& DA10_3_5 = +15467184783D0/13421772800D0,
& DA10_3_6 = -3942154371D0/4194304000D0,
& DA10_3_7 = +21125300879D0/50331648000D0,
& DA10_3_8 = -445562559D0/4194304000D0,
& DA10_3_9 = +111284620491D0/9395240960000D0,
& DA10_4_1 = -19796057D0/20480000D0,
& DA10_4_2 = -535553D0/6720000D0,
& DA10_4_3 = +63403D0/1280000D0,
& DA10_4_4 = +281941D0/960000D0,
& DA10_4_5 = 1D0 +9443D0/40960D0,
& DA10_4_6 = -219887D0/320000D0,
& DA10_4_7 = +754091D0/3840000D0,
& DA10_4_8 = -39121D0/960000D0,
& DA10_4_9 = +581419D0/143360000D0,
& DA10_5_1 = -1D0 -10781441377D0/53687091200D0,
& DA10_5_2 = +16856063921D0/29360128000D0,
& DA10_5_3 = -47031869203D0/50331648000D0,
& DA10_5_4 = +4439913787D0/4194304000D0,
& DA10_5_5 = -6247096241D0/13421772800D0,
& DA10_5_6 = 1D0 +447917913D0/838860800D0,
& DA10_5_7 = -11512558907D0/16777216000D0,
& DA10_5_8 = +560510849D0/4194304000D0,
& DA10_5_9 = -75322449683D0/5637144576000D0,
& DA10_6_1 = -14564721451D0/15728640000D0,
& DA10_6_2 = -109580619D0/573440000D0,
& DA10_6_3 = +15285519D0/65536000D0,
& DA10_6_4 = -4234511D0/49152000D0,
& DA10_6_5 = -3573501D0/10485760D0,
& DA10_6_6 = +84173553D0/81920000D0,
& DA10_6_7 = 484815179D0/983040000D0,
& DA10_6_8 = -3694911D0/16384000D0,
& DA10_6_9 = +114744591D0/7340032000D0,
& DA10_7_1 = -10378315789D0/10737418240D0,
& DA10_7_2 = -2207113739D0/12582912000D0,
& DA10_7_3 = +48853634347D0/83886080000D0,
& DA10_7_4 = -16701919087D0/12582912000D0,
& DA10_7_5 = +84761718349D0/40265318400D0,
& DA10_7_6 = -2054315207D0/838860800D0,
& DA10_7_7 = +120669802351D0/50331648000D0,
& DA10_7_8 = -1748617243D0/20971520000D0,
& DA10_7_9 = -22368269479D0/268435456000D0,
& DA10_8_1 = -1D0 -1349D0/16000D0,
& DA10_8_2 = +1349D0/1750D0,
& DA10_8_3 = -9443D0/3000D0,
& DA10_8_4 = +9443D0/1250D0,
& DA10_8_5 = -9443D0/800D0,
& DA10_8_6 = +9443D0/750D0,
& DA10_8_7 = -9443D0/1000D0,
& DA10_8_8 = +1349D0/250D0,
& DA10_8_9 = -466589D0/560000D0)
parameter(
& A210_1_1 = -225991639143D0/1342177280000D0,
& A210_1_2 = -121395173141D0/146800640000D0,
& A210_1_3 = +6468370013D0/3355443200D0,
& A210_1_4 = -22440146897D0/12582912000D0,
& A210_1_5 = +57418737523D0/40265318400D0,
& A210_1_6 = -17489295313D0/20971520000D0,
& A210_1_7 = +82495624981D0/251658240000D0,
& A210_1_8 = -193947079D0/2516582400D0,
& A210_1_9 = +15367501777D0/1879048192000D0,
& A210_2_1 = +359763461D0/1048576000D0,
& A210_2_2 = -133859921D0/114688000D0,
& A210_2_3 = +348820373D0/327680000D0,
& A210_2_4 = -15150619D0/16384000D0,
& A210_2_5 = +67553873D0/52428800D0,
& A210_2_6 = -44952727D0/49152000D0,
& A210_2_7 = +26201627D0/65536000D0,
& A210_2_8 = -8246437D0/81920000D0,
& A210_2_9 = +246865651D0/22020096000D0,
& A210_3_1 = -252810927377D0/805306368000D0,
& A210_3_2 = +28197945999D0/29360128000D0,
& A210_3_3 = -32441533071D0/16777216000D0,
& A210_3_4 = +114820943051D0/62914560000D0,
& A210_3_5 = -15467184783D0/13421772800D0,
& A210_3_6 = +3942154371D0/4194304000D0,
& A210_3_7 = -21125300879D0/50331648000D0,
& A210_3_8 = +445562559D0/4194304000D0,
& A210_3_9 = -111284620491D0/9395240960000D0,
& A210_4_1 = -683943D0/20480000D0,
& A210_4_2 = +535553D0/6720000D0,
& A210_4_3 = -63403D0/1280000D0,
& A210_4_4 = -281941D0/960000D0,
& A210_4_5 = -9443D0/40960D0,
& A210_4_6 = +219887D0/320000D0,
& A210_4_7 = -754091D0/3840000D0,
& A210_4_8 = +39121D0/960000D0,
& A210_4_9 = -581419D0/143360000D0,
& A210_5_1 = +10781441377D0/53687091200D0,
& A210_5_2 = -16856063921D0/29360128000D0,
& A210_5_3 = +47031869203D0/50331648000D0,
& A210_5_4 = -4439913787D0/4194304000D0,
& A210_5_5 = +6247096241D0/13421772800D0,
& A210_5_6 = -447917913D0/838860800D0,
& A210_5_7 = +11512558907D0/16777216000D0,
& A210_5_8 = -560510849D0/4194304000D0,
& A210_5_9 = +75322449683D0/5637144576000D0,
& A210_6_1 = -1163918549D0/15728640000D0,
& A210_6_2 = +109580619D0/573440000D0,
& A210_6_3 = -15285519D0/65536000D0,
& A210_6_4 = +4234511D0/49152000D0,
& A210_6_5 = +3573501D0/10485760D0,
& A210_6_6 = -84173553D0/81920000D0,
& A210_6_7 = +498224821D0/983040000D0,
& A210_6_8 = +3694911D0/16384000D0,
& A210_6_9 = -114744591D0/7340032000D0,
& A210_7_1 = -359102451D0/10737418240D0,
& A210_7_2 = +2207113739D0/12582912000D0,
& A210_7_3 = -48853634347D0/83886080000D0,
& A210_7_4 = +16701919087D0/12582912000D0,
& A210_7_5 = -84761718349D0/40265318400D0,
& A210_7_6 = +2054315207D0/838860800D0,
& A210_7_7 = -120669802351D0/50331648000D0,
& A210_7_8 = +22720137243D0/20971520000D0,
& A210_7_9 = +22368269479D0/268435456000D0,
& A210_8_1 = +1349D0/16000D0,
& A210_8_2 = -1349D0/1750D0,
& A210_8_3 = +9443D0/3000D0,
& A210_8_4 = -9443D0/1250D0,
& A210_8_5 = +9443D0/800D0,
& A210_8_6 = -9443D0/750D0,
& A210_8_7 = +9443D0/1000D0,
& A210_8_8 = -1349D0/250D0)
parameter(
& A210_8_9 = +1026589D0/560000D0,
& DB10_1_1 = +761073292818799D0/2720626900992000D0,
& DB10_1_2 = +557937353D0/1297296000D0,
& DB10_1_3 = -214412651D0/259459200D0,
& DB10_1_4 = +170436457D0/259459200D0,
& DB10_1_5 = -7282853D0/25945920D0,
& DB10_1_6 = -4668473D0/259459200D0,
& DB10_1_7 = +22494019D0/259459200D0,
& DB10_1_8 = -10434029D0/259459200D0,
& DB10_1_9 = +3345851D0/518918400D0,
& DB10_2_1 = +1183625282033D0/2975685672960D0,
& DB10_2_2 = +23930143D0/14189175D0,
& DB10_2_3 = -213517489D0/162162000D0,
& DB10_2_4 = +3230893D0/2027025D0,
& DB10_2_5 = -686209D0/405405D0,
& DB10_2_6 = +2420083D0/2027025D0,
& DB10_2_7 = -4396151D0/8108100D0,
& DB10_2_8 = +2038273D0/14189175D0,
& DB10_2_9 = -1918153D0/113513400D0,
& DB10_3_1 = +70530807725549D0/423208629043200D0,
& DB10_3_2 = +330413059D0/201801600D0,
& DB10_3_3 = -3305147D0/28828800D0,
& DB10_3_4 = +30733931D0/20592000D0,
& DB10_3_5 = -4993271D0/2882880D0,
& DB10_3_6 = +4741897D0/4118400D0,
& DB10_3_7 = -14566397D0/28828800D0,
& DB10_3_8 = +26359309D0/201801600D0,
& DB10_3_9 = -6083071D0/403603200D0,
& DB10_4_1 = +3304437553D0/11623772160D0,
& DB10_4_2 = +21369776D0/14189175D0,
& DB10_4_3 = +92756D0/289575D0,
& DB10_4_4 = +3454736D0/2027025D0,
& DB10_4_5 = -90373469D0/162162000D0,
& DB10_4_6 = +91376D0/2027025D0,
& DB10_4_7 = +6956D0/289575D0,
& DB10_4_8 = -251824D0/14189175D0,
& DB10_4_9 = +46493D0/14189175D0,
& DB10_5_1 = +6901687296484073D0/19044388306944000D0,
& DB10_5_2 = +115012739D0/72648576D0,
& DB10_5_3 = +628493D0/10378368D0,
& DB10_5_4 = +22584689D0/10378368D0,
& DB10_5_5 = -4595D0/741312D0,
& DB10_5_6 = +630493723D0/1297296000D0,
& DB10_5_7 = -3425557D0/10378368D0,
& DB10_5_8 = +5553389D0/72648576D0,
& DB10_5_9 = -1181891D0/145297152D0,
& DB10_6_1 = +160618157669D0/635830272000D0,
& DB10_6_2 = +198307D0/121275D0,
& DB10_6_3 = -9029D0/69300D0,
& DB10_6_4 = +44857D0/17325D0,
& DB10_6_5 = -2131D0/3465D0,
& DB10_6_6 = +37927D0/17325D0,
& DB10_6_7 = -976837D0/1386000D0,
& DB10_6_8 = +11197D0/121275D0,
& DB10_6_9 = -11197D0/970200D0,
& DB10_7_1 = +153681594740771D0/544125380198400D0,
& DB10_7_2 = +404839597D0/259459200D0,
& DB10_7_3 = +5425339D0/37065600D0,
& DB10_7_4 = +73758847D0/37065600D0,
& DB10_7_5 = +878107D0/3706560D0,
& DB10_7_6 = +48743857D0/37065600D0,
& DB10_7_7 = +39269149D0/37065600D0,
& DB10_7_8 = -335961817D0/1297296000D0,
& DB10_7_9 = -7219753D0/518918400D0,
& DB10_8_1 = +3956D0/14175D0,
& DB10_8_2 = +23552D0/14175D0,
& DB10_8_3 = -3712D0/14175D0,
& DB10_8_4 = +41984D0/14175D0,
& DB10_8_5 = -3632D0/2835D0,
& DB10_8_6 = +41984D0/14175D0,
& DB10_8_7 = -3712D0/14175D0,
& DB10_8_8 = +23552D0/14175D0,
& DB10_8_9 = -448403D0/1134000D0,
& B210_1_1 = +1037851801D0/33554432000D0,
& B210_2_1 = -3193083D0/26214400D0,
& B210_3_1 = +153048097D0/1342177280D0,
& B210_4_1 = +1349D0/102400D0,
& B210_5_1 = -2509046919D0/33554432000D0,
& B210_6_1 = +3762361D0/131072000D0,
& B210_7_1 = +52838981D0/6710886400D0,