CODE

!hello..this is a questions of newton iteration
!in this i need to generate the first 10 roots of the given equation F=theeta*(1/(1-(a*h/sigma)))

!as you can see that the equation is a function of theeta and i also been given an equation for theeta

! theeta=(1-1/(((n-0.5)**2)*(3.142**2)*(k**2)))*3.142*(n-0.5)

!annd now you can see that theeta is a function of n..that is the number of roots..for for the first root.i have n=1 and so on..10

!also i need to have the derivative of the function because it will be needed for the newton iteration

!DF=1/(cos(theeta**2)) as u c that it depends on theeta as well

! so u see that i need to have the roots(theeta) for each value of n..and all these values of rooots need to be stored in an array

!then having done all this..these values of roots will be needed to calculate the values of the fnal equation which i have ommited for now

! i have made three function subprograms for these equations that i have mentioned.and this subroutine..but i am getting errors and warnings

!please make corrections and add comments for identification so that i can know my mistakes




PROGRAM NEWTON

real theeta(10),f(100),df(100),eps

theeta(1)=0.1
EPS=0.00001

CALL NEWT(theeta,X,EPS)
STOP
END

!-------------------------------------------------!

SUBROUTINE NEWT(theeta,X,EPS)
real theeta(10),f(100),df(100)



integer L

do L=1,10

X=theeta(L)-(F(theeta(L))/DF(theeta(L)))




DO WHILE(ABS(X-theeta(L)) .GT. EPS)
theeta(L)=X
X=theeta(L)-(F(theeta(L))/DF(theeta(L)))
END DO
end do

RETURN
END




!--------------------------------

function theeta(n)

integer n(10)

real k,a,h,sigma,theeta
dimension theeta(10)

a=0.1
h=23.0
sigma=46.0


k=1-(a*h/sigma)

do i=1,10

theeta(i)=(1-1/(((i-0.5)**2)*(3.142**2)*(k**2)))*3.142*(i-0.5)


end do



return

end

!-------------------------------------------------------------------------


FUNCTION F(theeta)

real a,h,sigma,f(9),theeta(9)

integer m

a=0.1
h=23.0
sigma=46.0




do m=2,10

F(m)=theeta(m)*(1/(1-(a*h/sigma)))
enddo


WRITE(6,10)theeta,F
10 FORMAT(22X,F16.7,4X,F16.7)
RETURN
END

!-------------

FUNCTION DF(theeta)
real df(9),theeta(9)

integer j

do j=2,10

DF(j)=1/(cos(theeta(j)**2))

end do

RETURN
END

DIMENSION THEETA(10),DF(10),F(10),c(10),b(10),t(10),x1(10),z(10),sum_1(10), Tcenter(10),r(10)

REAL K,THEETA,DF,F,c,b,sum_1,x,z,T0, Tcenter,alpha,r
integer t,y,p,j,l,m
 			
 			
A = .1
H = 23.
SIGMA = 46.
Alpha=0.000012
K = 1.-(A*H/SIGMA)
EPS = .0001
T0=250.0+273.0



 
DO N=1,10
!
! First calculate THEETA value
!
         RN = N
          THEETA(N)=(1.-1./(((RN-0.5)**2)*(3.142**2)*(K**2)))*3.142*(RN-0.5)
!
! Then using that THEETA value -- get derivative
! conversion of degrees into radians

         r(n)=theeta(n)*3.142/180

           DF(N) = 1./COS(r(N)**2)
!
! Then using that same THEETA value -- get F
!
           F(N) = r(N)*(1./K)


!hence r is the value of angle in radians,df the derivative and f the function

            print*,r(n),df(n),f(n)




END DO
!
! The make next loop here to get closure on a root, since you got all
! 10 values for F,DF, etc.
!

!--------------------------------------------------

!---------------------------------------

!now here is where i am having problems and because of this it only executes upto the above results of r ,df and f and then the fortran stops responding

!what i want is that for EVERY vallue of   r    there would be a number of iterations and i should therefore get the root from the newtons formula for each value of r and i also want to know how many iterations where there for each value of r

! so for example if for a value of r of 1.511102e-02   there were ..lets say...4 iterations and athe result..that is..the root ..was 0.0015

!but i think there is something wrong with this do loop..please help identify and correct
  

m=0

 do l=1,10
  
       
       
     			    
					 10 m=m+1
 
                   x=r(l)-(f(r(l))/df(r(l)))

					 



                    if(abs(x-r(l)).lt.eps) goto 20 
					 


                     r(l)=x 

					 

 goto 10

  
20 x1(l)=x

print *,'The Root is',x1(l),'valu',m 

end do

!-----------------------------------------------------------------


do p=1,10

 
 C(p)=(4*sin(x1(p)))/(2*(x1(p))-sin(2*(x1(p))))



B(p)=(x1(p)*alpha**2)/(a**2)

   print*,c(p),b(p)

   end do


	do i=0,9

	t(i)=i*60

	print*,t(i)

	enddo


  
do j=1,10

 y=j-1
z(j)=-(b(j)*t(y))
sum_1(j)=(C(j)*z(j))



  Tc(j)=T0*((a*h)/(sigma))*sum_1(j)

  print*,sum_1(j)



  end do




end