Roots by Bisection Method

Introduction

Bisection method is one of the most ancient and surely the simplest method to find the root of a function. But it is relatively time consuming method. First, we must know an interval in which a root lies. Root is found by repeatedly bisecting an interval. Successive values converge on a root of function f(x) when we begin with a pair of values that bracket the root. Let's take the interval (x1, x2) , x3 is halfway between x1 and x2, x4 is halfway between x2 and x3. We always take the next x-value as the midpoint of the last pair that bracket the root : these values bracket the root when there is sign change of f(x) at the two points. We repeat the process until we converge to the root.

Using C programming language to solve a function by Bisection Method

/*  To determine the root of a function by Bisection Method */

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

float f(float x)
{
    return x*sin(x) + cos(x);                   /* A continuous equation between given interval*/
 
}


int main()
{
    float a,b,c,d,e;

    printf("\nEnter  the interval (a,b)\n");
    scanf("%f%f",&a,&b);

    printf("\nEnter the tolerance value\n");
    scanf("%f",&d);

    do
    {
        c = (a+b)/2;
        if(f(c) * f(a) < 0)
            b=c;
        else
            a=c;
    }while( fabs(a-b)>d||f(c)==0);

    printf("Root is %f",c);

    return 0;

}