Bisection Method C++ Program (with Output)

This program implements Bisection Method for finding real root of nonlinear function in C++ programming language.

In this C++ program, x0 & x1 are two initial guesses, e is tolerable error, f(x) is actual function whose root is being obtained using bisection method and x is variable which holds and bisected value at each iteration.

C++ Source Code: Bisection Method

``````
#include<iostream>
#include<iomanip>
#include<math.h>

/*
Defining equation to be solved.
Change this equation to solve another problem.
*/

#define f(x) cos(x) - x * exp(x)

using namespace std;

int main()
{
/* Declaring required variables */
float x0, x1, x, f0, f1, f, e;
int step = 1;

/* Setting precision and writing floating point values in fixed-point notation. */
cout<< setprecision(6)<< fixed;

/* Inputs */
up:
cout<<"Enter first guess: ";
cin>>x0;
cout<<"Enter second guess: ";
cin>>x1;
cout<<"Enter tolerable error: ";
cin>>e;

/* Calculating Functional Value */
f0 = f(x0);
f1 = f(x1);

/* Checking whether given guesses brackets the root or not. */
if( f0 * f1 > 0.0)
{
cout<<"Incorrect Initial Guesses."<< endl;
goto up;
}
/* Implementing Bisection Method */
cout<< endl<<"****************"<< endl;
cout<<"Bisection Method"<< endl;
cout<<"****************"<< endl;
do
{
/* Bisecting Interval */
x = (x0 + x1)/2;
f = f(x);

cout<<"Iteration-"<< step<<":\t x = "<< setw(10)<< x<<" and f(x) = "<< setw(10)<< f(x)<< endl;

if( f0 * f < 0)
{
x1 = x;
}
else
{
x0 = x;
}
step = step + 1;
}while(fabs(f)>e);

cout<< endl<< Root is: "<<  x<< endl;

return 0;
}
``````

Bisection Method C++ Program Output

```Enter first guess: 0
Enter second guess: 1
Enter tolerable error: 0.00001

****************
Bisection Method
****************
Iteration-1:     x =   0.500000 and f(x) =   0.053222
Iteration-2:     x =   0.750000 and f(x) =  -0.856061
Iteration-3:     x =   0.625000 and f(x) =  -0.356691
Iteration-4:     x =   0.562500 and f(x) =  -0.141294
Iteration-5:     x =   0.531250 and f(x) =  -0.041512
Iteration-6:     x =   0.515625 and f(x) =   0.006475
Iteration-7:     x =   0.523438 and f(x) =  -0.017362
Iteration-8:     x =   0.519531 and f(x) =  -0.005404
Iteration-9:     x =   0.517578 and f(x) =   0.000545
Iteration-10:    x =   0.518555 and f(x) =  -0.002427
Iteration-11:    x =   0.518066 and f(x) =  -0.000940
Iteration-12:    x =   0.517822 and f(x) =  -0.000197
Iteration-13:    x =   0.517700 and f(x) =   0.000174
Iteration-14:    x =   0.517761 and f(x) =  -0.000012
Iteration-15:    x =   0.517731 and f(x) =   0.000081
Iteration-16:    x =   0.517746 and f(x) =   0.000035
Iteration-17:    x =   0.517754 and f(x) =   0.000011
Iteration-18:    x =   0.517757 and f(x) =  -0.000000

Root is: 0.517757

```