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C Examples for dassl system and jacobian
C --------------------------------------
c Copyright INRIA
subroutine res1(t,y,ydot,delta,ires,rpar,ipar)
implicit double precision (a-h,o-z)
dimension y(*), ydot(*), delta(*),rpar(*)
neq=1
c
c check y to make sure that it is valid input.
c if y is less than or equal to zero, this is invalid input.
c
if (y(1) .le. 0.0d0) then
ires = -1
else
c
c call f to obtain f(t,y)
c
call f1(neq,t,y,delta)
c
c form f = f'-f(t,y)
c
do 10 i = 1,neq
delta(i) = ydot(i) - delta(i)
10 continue
endif
c
return
end
c
subroutine f1 (neq, t, y, ydot)
integer neq
double precision t, y, ydot
dimension y(*), ydot(*)
ydot(1) = ((2.0d0*log(y(1)) + 8.0d0)/t - 5.0d0)*y(1)
return
end
c
subroutine res2(t,y,ydot,delta,ires,rpar,ipar)
implicit double precision (a-h,o-z)
integer neq
dimension y(*), ydot(*), delta(*)
neq=2
c
c call f to obtain f(t,y)
c
call f2(neq,t,y,delta)
c
c form f = f'-f(t,y)
c
do 10 i = 1,neq
delta(i) = ydot(i) - delta(i)
10 continue
c
return
end
c
subroutine f2 (neq, t, y, ydot)
implicit double precision (a-h,o-z)
integer neq
double precision t, y, ydot
dimension y(*), ydot(*)
ydot(1) = y(2)
ydot(2) = 100.0d0*(1.0d0 - y(1)*y(1))*y(2) - y(1)
return
end
subroutine dres1(t,y,ydot,res,ires,rpar,ipar)
implicit double precision(a-h,o-z)
dimension y(*),ydot(*),res(*),rpar(*)
res(1) = ydot(1) + 10.0d0*y(1)
res(2) = y(2) + y(1) - 1.0d0
return
end
subroutine dres2(t,y,ydot,res,ires,rpar,ipar)
implicit double precision(a-h,o-z)
dimension y(*),ydot(*),res(*),rpar(*)
data alph1/1.0d0/, alph2/1.0d0/, ng/5/
do 10 j = 1,ng
do 10 i = 1,ng
k = i + (j - 1)*ng
d = -2.0d0*y(k)
if (i .ne. 1) d = d + y(k-1)*alph1
if (j .ne. 1) d = d + y(k-ng)*alph2
10 res(k) = d - ydot(k)
return
end
C Jacobian part
C --------------------------------------
subroutine jac2 (t, y, ydot, pd, cj, rpar, ipar)
implicit double precision (a-h,o-z)
integer nrowpd
double precision t, y, pd
parameter (nrowpd=2)
dimension y(2), pd(nrowpd,2)
c
c first define the jacobian matrix for the right hand side
c of the ode: f' = f(t,y) , i.e. df/dy)
c
pd(1,1) = 0.0d0
pd(1,2) = 1.0d0
pd(2,1) = -200.0d0*y(1)*y(2) - 1.0d0
pd(2,2) = 100.0d0*(1.0d0 - y(1)*y(1))
c
c next update the jacobian with the right hand side to form the
c dae jacobian: d(f'-f)/dy = df'/dy - df/dy = i - df/dy
c
pd(1,1) = cj - pd(1,1)
pd(1,2) = - pd(1,2)
pd(2,1) = - pd(2,1)
pd(2,2) = cj - pd(2,2)
c
return
end
subroutine djac1(t,y,yprime,pd,cj,rpar,ipar)
implicit double precision(a-h,o-z)
dimension y(*),yprime(*),pd(2,2)
pd(1,1) = cj + 10.0d0
pd(1,2) = 0.0d0
pd(2,1) = 1.0d0
pd(2,2) = 1.0d0
return
end
subroutine djac2(t,y,yprime,pd,cj,rpar,ipar)
implicit double precision(a-h,o-z)
dimension y(*), pd(11,*), yprime(*),rpar(*)
data alph1/1.0d0/, alph2/1.0d0/, ng/5/
data ml/5/, mu/0/, neq/25/
mband = ml + mu + 1
mbandp1 = mband + 1
mbandp2 = mband + 2
mbandp3 = mband + 3
mbandp4 = mband + 4
mbandp5 = mband + 5
do 10 j = 1,neq
pd(mband,j) = -2.0d0 - cj
pd(mbandp1,j) = alph1
pd(mbandp2,j) = 0.0d0
pd(mbandp3,j) = 0.0d0
pd(mbandp4,j) = 0.0d0
10 pd(mbandp5,j) = alph2
do 20 j = 1,neq,ng
20 pd(mbandp1,j) = 0.0d0
return
end
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