# C Program implementing the Bisection Method ( Numerical Computing )

Method 1:
This program in C is used to demonstrate bisection method.

Bisection method is one of the many root finding methods.
In this method we are given a function f(x) and we approximate 2 roots a and b for the function such that f(a).f(b)<0.
Then we find another point
c=(a+b)/2
if f(c)==0
then root=c;
else
if f(a).f(c)<0
b=c;
if f(b).f(c)<0
a=c;
and we repeat these steps for the given number of iterations.

### C Program implementing the Bisection Method

```#include"stdio.h"
#include"math.h"

double F(double x)
{
return(pow(x,3)+3*x-5);//This return the value of the function
}
int main()
{
printf("This program illustrates the bisection method in C\n");
printf("x^3 + 3*x - 5 = 0\n");
double x0,x1;
printf("Enter the first approximation to the root\n");
scanf("%lf",&x0);
printf("Enter the second approximation to the root\n");
scanf("%lf",&x1);
int iter;
printf("Enter the number of iterations you want to perform\n");
scanf("%d",&iter);
int ctr=1;
double l1=x0;
double l2=x1;
double r,f1,f2,f3;
//We check if the initail approximations are the root or not
if(F(l1)==0)
r=l1;
else
if(F(l2)==0)
r=l2;
else
{
while(ctr< =iter)
{//this is an implementation of the algorithm mentioned above
f1=F(l1);
r=(l1+l2)/2.0;
f2=F(r);
f3=F(l2);
if(f2==0)
{
r=f2;
break;
}
printf("The root after %d iteration is %lf\n",ctr,r);
if(f1*f2<0)
l2=r;
else
if(f2*f3<0)
l1=r;
ctr++;
}
}
printf("The approximation to the root is %lf",r);
getch();
}
/*A sample run of the program was carried out and the results were found as:-
This program illustrates the bisection method in C
x^3 + 3*x - 5 = 0
Enter the first approximation to the root
1
Enter the second approximation to the root
2
Enter the number of iterations you want to perform
9
The root after 1 iteration is 1.500000
The root after 2 iteration is 1.250000
The root after 3 iteration is 1.125000
The root after 4 iteration is 1.187500
The root after 5 iteration is 1.156250
The root after 6 iteration is 1.146025
The root after 7 iteration is 1.148438
The root after 8 iteration is 1.152344
The root after 9 iteration is 1.154297
The root is 1.154297
*/
```

Method 2: Source Code for Bisection Method
for equation f(x) = x^3 – 4*x – 9

```#include "math.h"
#include "conio.h"
float fun (float x)
{
return (x*x*x - 4*x - 9);
}
void bisection (float *x, float a, float b, int *itr)
/* this function performs and prints the result of one iteration */
{
*x=(a+b)/2;
++(*itr);
printf("Iteration no. %3d X = %7.5f\n", *itr, *x);
}
void main ()
{
int itr = 0, maxmitr;
float x, a, b, allerr, x1;
printf("\nEnter the values of a, b, allowed error and maximum iterations:\n");
scanf("%f %f %f %d", &a, &b, &allerr, &maxmitr);
bisection (&x, a, b, &itr);
do
{
if (fun(a)*fun(x) < 0)
b=x;
else
a=x;
bisection (&x1, a, b, &itr);
if (fabs(x1-x) < allerr)
{
printf("After %d iterations, root = %6.4f\n", itr, x1);
return 0;
}
x=x1;
}
while (itr < maxmitr);
printf("The solution does not converge or iterations are not sufficient");
return 1;
}
```