how to solve newton raphson method in c++.

newton raphson method is a method to solve equations in numerical techniques.

#include<iostream.h>

#include<conio.h>

#include<math.h>

const double epsilon=0.00001;

float f(float x)

{

float fx1;

fx1=pow(x,4)+pow(x,2)-80;

return fx1;

}

float f_dash(float x)

{

float fx2;

fx2=4*pow(x,3)+2*x;

return fx2;

}

void main()

{

cout.setf(ios::fixed);

cout.setf(ios::showpoint);

clrscr();

float x0,c;

cout<<"Enter initial approximation\n";

cout<<"x0=";

cin>>x0;

cout<<"\nx0\t\tf(x0)\t\tf'(x0)\t\tc\n";

cout<<endl;

c=x0-(f(x0)/f_dash(x0));

                while(fabs(x0-c)>=epsilon)

                {

                cout<<x0<<"\t"<<f(x0)<<"\t"<<f_dash(x0)<<"\t"<<c<<endl;

                x0=c;

                c=x0-(f(x0)/f_dash(x0));

                }

cout<<"\n\nThe final root is:";

cout<<c;

getch();

}

OUTPUT:

Enter initial approximation

x0=2.5

     x0                        f(x0)               f'(x0)                  c

2.500000        -34.687500      67.500000       3.013889

3.013889        11.593969       115.534729      2.913538

2.913538        0.546817        104.755745      2.908318

2.908318        0.001412        104.214531      2.908305

The final root is:  2.908305