Archive for March, 2012

This file contains one solution from

Bisection

Secant

Regular False

Newton

Fixed Point Iteration

Synthetic Division

QD Method

Link for online file: https://docs.google.com/spreadsheet/ccc?key=0Arryl0I1PQbVdEFuM1k0YVBTZF9SS21SUUpvZjc3aXc

x0 = 5;
x1 = x0;

fx0 = (3*x0+sin(x0)-exp(x0))
fx1 = (3+cos(x0)-exp(x0))

if(fx0 ~= 0 && fx1 ~= 0)
while(abs(x1 - x0) < 0.0000001 || abs(fx1) < 0.000001)
x1 = x0
x0 = x0 - (fx0/fx1)
end
end

#include<iostream.h>
#include<conio.h>
#include<math.h>

float f (float x)
{
	float fx1;
	fx1 = pow(x,3) + pow(x,2) - (3*x) - 3; // f(x) = x^3 - x^2 - 3x - 3;
	return (fx1);
}

void main()
{
	float x1,x2,x3;
	int count = 0;
	int iter;

	cout <<"Enter x1 = ";
	cin >> x1;
	cout <<"Enter x2 = ";
	cin >> x2;
	cout <<"Enter number of iterations = ";
	cin >> iter;

//	int fx1 = (x1^3) + (x1^2) - (3x1) - 3;
//	int fx2 = (x2^3) + (x2^2) - (3x2) - 3;
	do
	{
		if(count == iter)
		{
			break;
		}

		x3 = x1 - (f(x1)*((x1 - x2) / f(x1) - f(x2))); //This is formula of Regular false method

		cout <<"x1=" << x1 <<" | x2="<< x2 <<" | x3=" << x3 <<" | " << "  f(x1)=" << f(x1) << " |  f(x2)=" << f(x2) << " |  f(x3)=" << f(x3) << endl << endl;

		//float temp1 = f(x1);
		//float temp2 = f(x3);
		if( f(x1) * f(x3) < 0 )
		{
			x2 = x3;
		}
		else
		{
			x1 = x3;
		}
		count++;
	}
	while ( abs(x1 - x2) < 0.0000001 || f(x3) == 0 );

}

#include<iostream.h>
#include<conio.h>
#include<math.h>

double f(double x)
{

	return ((3*x)+ sin(x) - exp(x)); // f(x) = x^3 + sin(x) - e^x

}

void main(void)
{
	double x0 = 1, x1 = 2, x2 = 0;
	cout<<"x0 = " << x0 << " | x1 = " << x1 << " | x2 = " << x2 << endl;

		if(abs(f(x0)) < abs(x1))
		{
			x0 = x1;
		}
		cout<<"x0 = " << x0 << " | x1 = " << x1 << " | x2 = " << x2 << endl;

		do
		{
			x2 = x0 - f(x0)*(x0 - x1) / f(x0) - f(x1);

			x0 = x1;
			x1 = x2;

			cout<<"x0 = " << x0 << " | x1 = " << x1 << " | x2 = " << x2 << endl;

		}
		while(abs(f(x2)) < 0.000000000001);

}