Regula Falsi or False Position Method Using C++

Table of Contents

• C++ Program
• Program Output
• Recommended Readings

This program implements false position (Regula Falsi) method for finding real root of nonlinear function in C++ programming language.

In this C++ program, x0 & x1 are two initial guesses, e is tolerable error and f(x) is non-linear equation whose root is being obtained using Regula Falsi method.

C++ Source Code: Regula Falsi Method

#include<iostream>
#include<iomanip>
#include<math.h>

/*
 Defining equation to be solved.
 Change this equation to solve another problem.
*/

#define f(x) cos(x) - x * exp(x)

using namespace std;

int main()
{
	 /* Declaring required variables */
	 float x0, x1, x, f0, f1, f, e;
	 int step = 1;

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

	 /* Inputs */
	 up:
	 cout<<"Enter first guess: ";
     cin>>x0;
     cout<<"Enter second guess: ";
     cin>>x1;
     cout<<"Enter tolerable error: ";
     cin>>e;

	 /* Calculating Functional Value */
	 f0 = f(x0);
	 f1 = f(x1);

	 /* Checking whether given guesses brackets the root or not. */
	 if( f0 * f1 > 0.0)
	 {
		  cout<<"Incorrect Initial Guesses."<< endl;
		  goto up;
	 }
   /* Implementing False Position Method */
     cout<< endl<<"*********************"<< endl;
	 cout<<"False Position Method"<< endl;
	 cout<<"*********************"<< endl;
	 do
	 {
		  /* Applying False Position Method */
		  /* x is next approximated root using False Position method */
		  x = x0 - (x0-x1) * f0/ (f0-f1);
		  f = f(x);

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

		  if( f0 * f < 0)
		  {
			   x1 = x;
			   f1 = f;
		  }
		  else
		  {
			   x0 = x;
			   f0 = f;
		  }
		  step = step + 1;
	 }while(fabs(f)>e);

	 cout<< endl<<"Root is: "<< x<< endl;

	 return 0;
}

False Position C++ Program Output

	
Enter first guess: 0
Enter second guess: 1
Enter tolerable error: 0.00001

*********************
False Position Method
*********************
Iteration-1:     x =   0.314665 and f(x) =   0.519871
Iteration-2:     x =   0.446728 and f(x) =   0.203545
Iteration-3:     x =   0.494015 and f(x) =   0.070802
Iteration-4:     x =   0.509946 and f(x) =   0.023608
Iteration-5:     x =   0.515201 and f(x) =   0.007760
Iteration-6:     x =   0.516922 and f(x) =   0.002539
Iteration-7:     x =   0.517485 and f(x) =   0.000829
Iteration-8:     x =   0.517668 and f(x) =   0.000271
Iteration-9:     x =   0.517728 and f(x) =   0.000088
Iteration-10:    x =   0.517748 and f(x) =   0.000029
Iteration-11:    x =   0.517754 and f(x) =   0.000009

Root is: 0.517754