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

Table of Contents

• C++ Source Code
• Program Output
• Recommended Readings

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

In this C++ program, x0 is initial guess, e is tolerable error, f(x) is actual function whose root is being obtained using Newton Raphson 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<iostream>
#include<iomanip>
#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)

using namespace std;

int main()
{
	 float x0, x1, f0, f1, g0, e;
	 int step = 1, N;

	 /* Setting precision and writing floating point values in fixed-point notation. */
     cout<< setprecision(6)<< fixed;

     /* Inputs */
	 cout<<"Enter initial guess: ";
	 cin>>x0;
	 cout<<"Enter tolerable error: ";
	 cin>>e;
	 cout<<"Enter maximum iteration: ";
	 cin>>N;

	 /* Implementing Newton Raphson Method */
	 cout<< endl<<"*********************"<< endl;
	 cout<<"Newton Raphson Method"<< endl;
	 cout<<"*********************"<< endl;
	 do
	 {
		  g0 = g(x0);
		  f0 = f(x0);
		  if(g0 == 0.0)
		  {
			   cout<<"Mathematical Error.";
			   exit(0);
		  }


		  x1 = x0 - f0/g0;


		  cout<<"Iteration-"<< step<<":\t x = "<< setw(10)<< x1<<" and f(x) = "<< setw(10)<< f(x1)<< endl;
		  x0 = x1;

		  step = step+1;

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

		  f1 = f(x1);

	 }while(fabs(f1)>e);

	 cout<< endl<<"Root is: "<< x1;
	 return 0;
}

Newton Raphson C++ Output

Enter initial guess: 2
Enter tolerable error: 0.000001
Enter maximum iteration: 10

*********************
Newton Raphson Method
*********************
Iteration-1:     x1 =   0.614547 and f(x1) =   0.026607
Iteration-2:     x1 =   0.607108 and f(x1) =   0.000023
Iteration-3:     x1 =   0.607102 and f(x1) =  -0.000000

Root is: 0.607102