# Regula Falsi or False Position Method Using C++

#### 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
```