Explain Bisection Method with source code

BISECTION METHOD:

Algorithm:

a)      assign two initial values x1 and x2 and stopping criteria (or prescribed error) as E.

b)      calculate f(x1) and f(x2)

c)       if f(x1)*f(x2)>0 then x1 and x2 do not bracket the root, go to step (g) otherwise continue

d)      compute: xm=(x1+x2)/2 and f(xm)

e)      if f(x1)*f(xm)<0 then

set x2=xm

else

set x1=xm

f)       if |x1-x2|/x2<E

then root= x1+x2/2

print the value of root

else

goto step (d)

g)      STOP

Assumptions:

a)      any non-linear equation is defined as macro.

b)      Estimated precision of error is defined as E.

c)       Required data type is float.

d)      The program coded to solve the equation            x³-5x+1=0

Source code:

#include<stdio.h>

#include<conio.h>

#include<math.h>

#define f(x) x*x*x-5*x+1

#define E 0.00001

void main()

{

float x1, x2, f1, f2, xm, f3, root;

clrscr();

printf(“enter the initial values of x1 and x2:”);

scanf(“%f%f”, &x1, &x2);

f1=f(x1);

f2=f(x2);

if((f1*f2)>0)

printf(“x1 and x2 do not bracket the root:”);

else

{

here: xm=(x1+x2)/2;

           f3=f(xm);

}

if((f1*f3)<0)

{

x2=xm;

}

else

{

x1=xm;

}

if(fabs(x1-x2)<E)

{

float root=xm;

printf(“the root is %f”, root);

}

else

{

goto here;

}

getch();

}