NEWTON RAPHSON METHOD

Finding The Roots Of The Given Equation By Using Newton Raphson Method

Source code :-

// Solve by Newton Raphson method [ X^3-3X^2+2X-5=0 ]

#include <stdio.h>
#include <math.h>
float f(float x)
{
    return (pow(x, 3) - 3 * x * x + 2 * x - 5); // Replace With given Equation
}
float fd(float x)
{
    return (3 * pow(x, 2) - 6 * x + 2); // Replace With given Equation
}
float fdd(float x)
{
    return (6 * x - 6); // Replace With given Equation
}
int main()
{
    float h, x, y, err;
    int n = 0, d;
    do
    {
        printf("Enter an approximate root: ");
        scanf("%f", &x);
        if (fabs(f(x) * fdd(x)) < (fd(x) * fd(x)))
            break;
        else
            printf("\nWrong value entered!!!try again...\n");
    } while (1);
    printf("\nEnter the correction upto decimal place: ");
    scanf("%d", &d);
    err = (5.0 / pow(10, d));
    printf("\nIter\t   Xn\t\t  f(Xn)\t\t  f'(Xn)\t   Hn\t\tXn+1=Xn+Hn\n");
    printf("----------------------------------------------------------------------------------\n");        
    y = x;
    h = f(x) / fd(x);
    x = x - h;
    printf(" %2d\t%+f\t%+f\t%+f\t%+f\t%+f\n", ++n, y, f(y), fd(y), h, x);
    while (fabs(x - y) >= err)
    {
        y = x;
        h = f(x) / fd(x);
        x = x - h;
        printf(" %2d\t%+f\t%+f\t%+f\t%+f\t%+f\n", ++n, y, f(y), fd(y), h, x);
    }
    printf("\n\nThe root is: %f", x);
    return 1;
}

Input-Output :-

abhi@hp-15q-laptop:~$ gcc raphson.c
abhi@hp-15q-laptop:~$ ./a.out

Enter an approximate root: 4

Enter the correction upto decimal place: 5

Iter       Xn             f(Xn)           f'(Xn)           Hn           Xn+1=Xn+Hn
----------------------------------------------------------------------------------
  1     +4.000000       +19.000000      +26.000000      +0.730769       +3.269231        
  2     +3.269231       +4.415967       +14.448226      +0.305641       +2.963590
  3     +2.963590       +0.607399       +10.567060      +0.057480       +2.906110
  4     +2.906110       +0.019273       +9.899764       +0.001947       +2.904163
  5     +2.904163       +0.000022       +9.877510       +0.000002       +2.904161


The root is: 2.904161