! 	  From: "COMPUTATIONAL PHYSICS, 2nd Ed" 
! 		by RH Landau, MJ Paez, and CC Bordeianu 
! 		Copyright Wiley - VCH, 2007.
! 		Electronic Materials copyright: R Landau, Oregon State Univ, 2007;
! 		MJ Paez, Univ Antioquia, 2007; and CC Bordeianu, Univ Bucharest, 2007.
! 		Supported by the US National Science Foundation
! 		
! Newton_cd.f90: Newton-Raphson root finder, central diff derivative
! 
Program Newton_cd

  Implicit none
  Integer :: it, imax = 10   ! Maximum number of iterations permitted
  Real*8 :: x, dx = 1e - 2, eps = 1e - 6, f1, df, F 
	
	                                   ! x guess, must be close to root
  x = 2.                                   
  Do	it = 0, imax
	  f1	 = 	F(x)                             ! Compute Function value
		write(*, *) it, x, f1
		                                  ! Central difference derivative
		df = ( F(x + dx/2) - F(x - dx/2) )/dx	  
		dx	 = 	 - f1/df
		x = 	x + dx													                ! New guess
		                                          ! Check for convergence
		If ( abs(F(x))  <= eps	 ) then                 
		  write(*, *) eps
		  Stop
	  Endif
  End Do
End Program Newton_cd

Function F(x)			 
  Implicit none
  Real*8 :: x, F			
  F = 2*cos(x) - x
End