C program of Newton Raphson Method | C code champ

C program of Newton Raphson Method : Newton Raphson method is a method of approximating a root of the polynomial equation also called the method of tangents. In Newton’s method, the initial (“first”) approximation x = a₁ is used to find a second, more accurate, approximation by drawing the tangent to the graph of y = f(x) at the point A[a₁, f(a₁)] up to the intersection of the tangent with the x-axis. The point of intersection is

                                                                                     x = a₁ – f(a₁)/f’(a₁)

and is adopted as the new value a₂ of the root. By repeating this process as necessary, we can obtain increasingly accurate approximations a₂, a₃, … of the root provided that the derivative f’(x) is monotonic and preserves its sign on the segment containing root.

How to use the C program :

Consider an example : f(x) = x^2   -  4  as our polynomial equation. We want to calculate its root and say first approximation =6. Then maximum power of X = 2, coefficients of x^0  = -4,  x^1 = 0,  x^2  = 1  & first approximation =6. Now C program of Newton Raphson Method will display the iterations and root of the polynomial as output.

C program of Newton Raphson Method :

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

int max_power,i=0,cnt=0,flag=0;
int coef[10]={0};
float x1=0,x2=0,t=0;
float fx1=0,fdx1=0;

int main()
{

    printf("-----------------------------------------------------------\n");
    printf("----------------------Made by C code champ-----------------\n");
    printf("-----------------------------------------------------------\n\n");
    printf("\n\n\t C PROGRAM FOR NEWTON RAPHSON METHOD");

    printf("\n\n\n\tENTER THE MAXIMUM POWER OF X = ");
    scanf("%d",&max_power);

    for(i=0;i<=max_power;i++)
    {
        printf("\n\t x^%d = ",i);
        scanf("%d",&coef[i]);
    }

    printf("\n");

    printf("\n\tTHE POLYNOMIAL IS = ");
    for(i=max_power;i>=0;i--)/*printing coefficients*/
    {
        printf(" %dx^%d",coef[i],i);
    }

    printf("\n\n\tFirst approximation x1 ----> ");
    scanf("%f",&x1);

     printf("\n\n-----------------------------------------------------------\n");
     printf("\n ITERATION \t x1 \t F(x1) \t \tF'(x1)  ");
     printf("\n-----------------------------------------------------------\n");

    do
    {
            cnt++;
            fx1=fdx1=0;
            for(i=max_power;i>=1;i--)
            {
                fx1+=coef[i] * (pow(x1,i)) ;
            }
            fx1+=coef[0];
            for(i=max_power;i>=0;i--)
            {
                fdx1+=coef[i]* (i*pow(x1,(i-1)));
            }
            t=x2;
            x2=(x1-(fx1/fdx1));

            x1=x2;

            printf("\n\t %d \t%.3f \t %.3f\t\t%.3f ",cnt,x2,fx1,fdx1);

    }while((fabs(t - x1))>=0.0001);
    printf("\n\n\n\t THE ROOT OF EQUATION IS = %f",x2);
    getch();
}

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