# Secant Method Python Program with Output

#### This program implements Secant Method for finding real root of nonlinear equation in python programming language.

In this python program, x0 & x1 are two initial guess values, e is tolerable error and f(x) is actual non-linear function whose root is being obtained using secant method. Variable x2 holds approximated root in each step.

## Python Source Code: Secant Method

``````
# Defining Function
def f(x):
return x**3 - 5*x - 9

# Implementing Secant Method

def secant(x0,x1,e,N):
print('\n\n*** SECANT METHOD IMPLEMENTATION ***')
step = 1
condition = True
while condition:
if f(x0) == f(x1):
print('Divide by zero error!')
break

x2 = x0 - (x1-x0)*f(x0)/( f(x1) - f(x0) )
print('Iteration-%d, x2 = %0.6f and f(x2) = %0.6f' % (step, x2, f(x2)))
x0 = x1
x1 = x2
step = step + 1

if step > N:
print('Not Convergent!')
break

condition = abs(f(x2)) > e
print('\n Required root is: %0.8f' % x2)

# Input Section
x0 = input('Enter First Guess: ')
x1 = input('Enter Second Guess: ')
e = input('Tolerable Error: ')
N = input('Maximum Step: ')

# Converting x0 and e to float
x0 = float(x0)
x1 = float(x1)
e = float(e)

# Converting N to integer
N = int(N)

#Note: You can combine above three section like this
# x0 = float(input('Enter First Guess: '))
# x1 = float(input('Enter Second Guess: '))
# e = float(input('Tolerable Error: '))
# N = int(input('Maximum Step: '))

# Starting Secant Method
secant(x0,x1,e,N)

``````

## Python Program Output: Secant Method

```Enter First Guess: 2
Enter Second Guess: 3
Tolerable Error: 0.000001
Maximum Step: 10

*** SECANT METHOD IMPLEMENTATION ***
Iteration-1, x2 = 2.785714 and f(x2) = -1.310860
Iteration-2, x2 = 2.850875 and f(x2) = -0.083923
Iteration-3, x2 = 2.855332 and f(x2) = 0.002635
Iteration-4, x2 = 2.855196 and f(x2) = -0.000005
Iteration-5, x2 = 2.855197 and f(x2) = -0.000000

Required root is: 2.85519654
```