# Newton-Raphson Method

False Position Method

This method is known as Bolzano method, bracketing method, binary chopping method or half interval method.

Suppose we are given the continuous function f(x) in the interval [p, q] and we want to find root of the equation f(x)=0 by bisection method. The process is described as follows:-

1)      Find two points a and b such that f(a) * f(b) < 0. That is find a and b so that f(a) and f(b) are of opposite sign. This process is called finding the initial root.
2)      Compute the middle point c using relation c= (a+b)/2. If f(c) = 0 then ‘c’ is the required root & stop the process if f (c) 0 then go to next step.
3)      If f(a) * f (c) <0 then root lies between a & c otherwise the root lies between c & b.
4)      Repeat step 2 & 3 until the root is found to be desired of accuracy.

#include<stdio.h>
#include<conio.h>
float f(float x){
return (x*x*x-4*x-9);
}
void main(){
int i,n;
float a,b,c;
clrscr();
printf("Enter the no of iteration:");
scanf("%d",&n);
printf("enter two values where the root lies:");
scanf("%f %f",&a,&b);
if(f(a)*f(b)>0)
{
printf("the initial values are out of range");
getch();
exit(0);
}
else{
for(i=1;i<=n;i++){
c=(a+b)/2;
if(f(c)==0)
break;
if(f(a)*f(c)<0)
b=c;
else
a=c;
}
printf("the reqd. root is:%f",c);
getch();
}
}

Bisection Method || numerical Method Reviewed by Santosh Adhikari on October 04, 2018 Rating: 5