False Position Method Python Program (with Output)

Table of Contents

• Python Program
• Program Output
• Recommended Readings

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

In this python program, x0 and x1 are two initial guesses, e is tolerable error and nonlinear function f(x) is defined using python function definition def f(x):.

Python Source Code: False Position (Regula Falsi) Method

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

# Implementing False Position Method
def falsePosition(x0,x1,e):
    step = 1
    print('\n\n*** FALSE POSITION METHOD IMPLEMENTATION ***')
    condition = True
    while condition:
        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)))

        if f(x0) * f(x2) < 0:
            x1 = x2
        else:
            x0 = x2

        step = step + 1
        condition = abs(f(x2)) > e

    print('\nRequired root is: %0.8f' % x2)


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

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

#Note: You can combine above two section like this
# x0 = float(input('First Guess: '))
# x1 = float(input('Second Guess: '))
# e = float(input('Tolerable Error: '))


# Checking Correctness of initial guess values and false positioning
if f(x0) * f(x1) > 0.0:
    print('Given guess values do not bracket the root.')
    print('Try Again with different guess values.')
else:
    falsePosition(x0,x1,e)

False Position Program Output

First Guess: 2
Second Guess: 3
Tolerable Error: 0.00001


*** FALSE POSITION 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 = 2.854933 and f(x2) = -0.005125
Iteration-4, x2 = 2.855180 and f(x2) = -0.000312
Iteration-5, x2 = 2.855196 and f(x2) = -0.000019
Iteration-6, x2 = 2.855196 and f(x2) = -0.000001

Required root is: 2.85519648