/* 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.
	 Support by National Science Foundation															 
	 */
// Newton_fd.java: Newton-Raphson root finder with forward diff deriv

public class Newton_fd	{ 
	
	public static double f(double x) {				 // Function to find zero
		return 2*Math.cos(x)-x; }
		
	public static void main(String[] argv) {	 
		
		double eps = 1e-6;																 	 // Tolerance
		double df, x = 2., dx = 1e-2; ;		 
		int it, imax = 100;												// Max no of iterations
		                                                    // Iterations
		for ( it=1;	 it <= imax;	it++ )	{
			                                     // Forward diff derivative
			df = ( f(x + dx) - f(x))/dx;			 
			dx = -f(x)/df; 
			x += dx;																					 // New guess
			System.out.println("Iterate #= "+it+"	x = "+x+" f(x)= "+f(x)); 
			                                       // Check for convergence
			if ( Math.abs(f(x)) <= eps )	{						 
				System.out.println("Root found with precison = " + eps); 
				break; 
} } } }