How Can I Correct My Fortran Program for Newton's Method?

[jjohnson8]

I'm working on a program for Newton's method for solving equations.

This is my code:

=======================================================
program Newton
implicit real(a-h,o-z)
F(x) = x**2 - 4
!...&---1---------2---------3---------4---------5---------6---------7---

!----All values to be read in/set values----!
PRINT*, 'Please inter initial guess for root: '
READ*, x0
maxIT = 20
TOL = 1.e-14
EPS = 1.e-14
xn = 0
!----Print titles for output----!
PRINT 20, 'x0', 'maxIT', 'TOL', 'EPS', 'n', 'xn', 'F(xn)'

!----Do Loop to go from 0 to max iterations----!
DO n = 0,maxIT
CALL FCN(xn, Fn, DFn)
xn = x0 - (Fn/DFn)
Dx = xn - x0
x0 = xn
IF( ABS(Dx) .LE. TOL) THEN
IF( ABS(Fn) .LE. TOL) THEN
PRINT*, 'DONE: root=',xn,' found in',n,'iterations'
PRINT*, ' residual =', Fn
ELSE
PRINT*, 'Stuck at iteration:', n
PRINT*, ' relDX < EPS but residual=',Fn,' > TOL, exiting'
STOP
ENDIF
ENDIF
PRINT 10, x0, maxIT, TOL, EPS, n, xn, F(xn)
ENDDO
!----Formats for headings----!
10 FORMAT(F10.7,4x,I2,4x,F18.14,13x,F18.14,8x,I2,3x,F10.7,3x,F10.7)
20 FORMAT(A2,10x,A5,8x,A3,35x,A3,10x,A1,6x,A2,11x,A5)
END

subroutine FCN(xn, Fn, DFn)
Fn = (x0**2) - 4
DFn = 2*x0
return
END


Here is my output:

x0 maxIT TOL EPS n xn F(xn)
+Infinity 20 0.00000000000001 0.00000000000001 0 +Infinity +Infinity
+Infinity 20 0.00000000000001 0.00000000000001 1 +Infinity +Infinity
+Infinity 20 0.00000000000001 0.00000000000001 2 +Infinity +Infinity
+Infinity 20 0.00000000000001 0.00000000000001 3 +Infinity +Infinity
+Infinity 20 0.00000000000001 0.00000000000001 4 +Infinity +Infinity
+Infinity 20 0.00000000000001 0.00000000000001 5 +Infinity +Infinity
+Infinity 20 0.00000000000001 0.00000000000001 6 +Infinity +Infinity
+Infinity 20 0.00000000000001 0.00000000000001 7 +Infinity +Infinity
+Infinity 20 0.00000000000001 0.00000000000001 8 +Infinity +Infinity
+Infinity 20 0.00000000000001 0.00000000000001 9 +Infinity +Infinity
+Infinity 20 0.00000000000001 0.00000000000001 10 +Infinity +Infinity
+Infinity 20 0.00000000000001 0.00000000000001 11 +Infinity +Infinity
+Infinity 20 0.00000000000001 0.00000000000001 12 +Infinity +Infinity
+Infinity 20 0.00000000000001 0.00000000000001 13 +Infinity +Infinity
+Infinity 20 0.00000000000001 0.00000000000001 14 +Infinity +Infinity
+Infinity 20 0.00000000000001 0.00000000000001 15 +Infinity +Infinity
+Infinity 20 0.00000000000001 0.00000000000001 16 +Infinity +Infinity
+Infinity 20 0.00000000000001 0.00000000000001 17 +Infinity +Infinity
+Infinity 20 0.00000000000001 0.00000000000001 18 +Infinity +Infinity
+Infinity 20 0.00000000000001 0.00000000000001 19 +Infinity +Infinity
+Infinity 20 0.00000000000001 0.00000000000001 20 +Infinity +Infinity


I've tinkered with this all day, and I can't figure out how to get anything different than infinity for the values. Anyone out there that can correct me?

 

[Dr Transport]

Looks like you're not passing xn, the function should be

subroutine FCN(xn, Fn, DFn)
Fn = (xn**2) - 4
DFn = 2*xn
return

also try making tol and eps larger...