# C Program for Newton Raphson (NR) Method (with Output)

#### This program implements Newton Raphson method for finding real root of nonlinear equation in C programming language.

In this C program, x0 is initial guess value, e is tolerable error and f(x) is non-linear function whose root is being obtained using Newton method.

## C Source Code: Newton Raphson Method

``````
/* Program: Finding real roots of nonlinear
equation using Newton Raphson Method
Author: CodeSansar
Date: November 18, 2018 */
#include<stdio.h>
#include<conio.h>
#include<math.h>
#include<stdlib.h>

/* Defining equation to be solved.
Change this equation to solve another problem. */
#define    f(x)    3*x - cos(x) -1

/* Defining derivative of g(x).
As you change f(x), change this function also. */
#define   g(x)   3 + sin(x)

void main()
{
float x0, x1, f0, f1, g0, e;
int step = 1, N;
clrscr();
/* Inputs */
printf("\nEnter initial guess:\n");
scanf("%f", &x0);
printf("Enter tolerable error:\n");
scanf("%f", &e);
printf("Enter maximum iteration:\n");
scanf("%d", &N);
/* Implementing Newton Raphson Method */
printf("\nStep\t\tx0\t\tf(x0)\t\tx1\t\tf(x1)\n");
do
{
g0 = g(x0);
f0 = f(x0);
if(g0 == 0.0)
{
printf("Mathematical Error.");
exit(0);
}

x1 = x0 - f0/g0;

printf("%d\t\t%f\t%f\t%f\t%f\n",step,x0,f0,x1,f1);
x0 = x1;

step = step+1;

if(step > N)
{
printf("Not Convergent.");
exit(0);
}

f1 = f(x1);

}while(fabs(f1)>e);

printf("\nRoot is: %f", x1);
getch();
}
``````

## Output: Newton Raphson Method Using C

```Enter initial guess:
1
Enter tolerable error:
0.00001
Enter maximum iteration:
10

Step            x0              f(x0)           x1              f(x1)
1               1.000000        1.459698        0.620016        0.000000
2               0.620016        0.046179        0.607121        0.046179
3               0.607121        0.000068        0.607102        0.000068

Root is: 0.607102
```