!   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_fd.f90:Newton-Raphson root finder, forward diff derivative
! 
Program NewtonRHL_fd

  Implicit none
  Integer :: it, imax = 10                    ! Max number iterations
  Real*8 :: x, dx = 1e - 2, eps = 1e - 6, df, F  
	
	                                              ! Guess must be close
  x = 2.                                              
  Do	it = 1, imax
	                                    ! Forward difference derivative
	  df = ( F(x + dx) - F(x) )/dx			      
		dx	 = 	 - F(x)/df
		x = 	x + dx													                ! New guess
		write(*, *) it, x, F(x)
		                                          ! Check for convergence
		If ( abs(F(x)) <= eps	 ) then                   
		  write(*, *) eps
		  Stop
		Endif
  End Do
End
                                         ! Find zero of this function
function F(x)		                               
  Implicit none
  Real*8 :: x, F			
  F = 2*cos(x) - x
End