PROGRAM (TO FIND APPROXIMATE ROOT OF THE LINEAR EQUATION BY NEWTON-RAPHSON METHOD)

PROGRAM

FINDING APPROXIMATE ROOT OF A LINEAR EQUATION BY NEWTON-RAPHSON METHOD

#include<stdio.h>

#include<math.h>

#include<conio.h>

float f(float x)

{

 return (x*x)-2*x;

}

float df(float y)

{

 return(2*y)-2;

}

int main()

{

 float x0,x1,h;

 int n;

 clrscr();

 printf("\nenter the max no. of iterations");

 scanf("%d",&n);

 printf("\nenter the initial approximate value for the function (x*x)-(2*x)");

 scanf("%f",&x0);

 for(int i=0;i<n;i++)

 {

  h=f(x0)/df(x0);

  x1=x0-h;

  printf("\n at the iteration %d, root is %f\n",(i+1),x1);

  if(fabs(h)<0.001)

  {

   printf("\nafter %d iteration final root is %f",(i+1),x1);

  }

  x0=x1;

 }

 getch();

 return 0;

}

OUTPUT:-

PROGRAM (TO FIND APPROXIMATE ROOT OF A LINEAR EQUATION BY BISECTION METHOD)

PROGRAM

FINDING APPROXIMATE ROOT OF A LINEAR EQUATION BY BISECTION

#include<stdio.h>

#include<math.h>

#include<conio.h>

float f(float x)

{

 return (x*x*x)-4*x-9;

}

int main()

{

 float x0,x1,a,b;

 int i=1,n;

 clrscr();

 printf("\nenter the values of a, b and max no. of iterations\n");

 scanf("%f %f %d",&a,&b,&n);

 x0=(a+b)/2;

 printf("\nat iteration %d, root is x= %f\n",i,x0);

 i++;

 while(i<=n)

 {

  if(f(a)*f(x0)<0)

  b=x0;

  else

  a=x0;

  x1=(a+b)/2;

  printf("at intersect %d, root is x=%f\n",i,x1);

  if(fabs(x1-x0)<0.001)

  {

   printf("after %d iterations, the value of root is %f\n",i,x1);

   break;

  }

  x0=x1;

  i++;

 }

 getch();

 return 0;

}

OUTPUT:-