//http://www.timestocome.com
//linda macphee-cobb
//solve an de function using bisection

#include <stdio.h>
#include <math.h>

#define PI 3.14159

void main (void){

	double middle, fleft, fright, fmiddle;
	double error = 1.0, left = 0.0, right = PI/2.0, tol = 0.001;
	
	//function:>  f(x) = cos(x) - x

	fleft = cos(left) - left;
	fright = cos(right) - right;

	while(error > tol){

	middle = (left+right)/2.0;
	fmiddle = cos(middle)-middle;

	//which half of interval has the root
	if((fleft * fmiddle) < 0){			//root is in left
		right = middle;
		fright = fmiddle;
	}else{								//root is in right
		left = middle;
		fleft = fmiddle;
	}

	//root now between new left and right
	//so check for error tolerance and redo or
	//return answer

	error = sqrt(((right-left)/middle)*((right-left)/middle));
	
	
	}

	printf("\n the solution is %lf", middle);
	getchar();
}