Bisection Method Python Program (with Output)

Table of Contents

This program implements Bisection 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: Bisection Method


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

# Implementing Bisection Method
def bisection(x0,x1,e):
    step = 1
    print('\n\n*** BISECTION METHOD IMPLEMENTATION ***')
    condition = True
    while condition:
        x2 = (x0 + x1)/2
        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 bisecting
if f(x0) * f(x1) > 0.0:
    print('Given guess values do not bracket the root.')
    print('Try Again with different guess values.')
else:
    bisection(x0,x1,e)

Bisection Method Python Program Output

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


*** BISECTION METHOD IMPLEMENTATION ***
Iteration-1, x2 = 2.500000 and f(x2) = -5.875000
Iteration-2, x2 = 2.750000 and f(x2) = -1.953125
Iteration-3, x2 = 2.875000 and f(x2) = 0.388672
Iteration-4, x2 = 2.812500 and f(x2) = -0.815186
Iteration-5, x2 = 2.843750 and f(x2) = -0.221588
Iteration-6, x2 = 2.859375 and f(x2) = 0.081448
Iteration-7, x2 = 2.851562 and f(x2) = -0.070592
Iteration-8, x2 = 2.855469 and f(x2) = 0.005297
Iteration-9, x2 = 2.853516 and f(x2) = -0.032680
Iteration-10, x2 = 2.854492 and f(x2) = -0.013700
Iteration-11, x2 = 2.854980 and f(x2) = -0.004204
Iteration-12, x2 = 2.855225 and f(x2) = 0.000546
Iteration-13, x2 = 2.855103 and f(x2) = -0.001829
Iteration-14, x2 = 2.855164 and f(x2) = -0.000641
Iteration-15, x2 = 2.855194 and f(x2) = -0.000048
Iteration-16, x2 = 2.855209 and f(x2) = 0.000249
Iteration-17, x2 = 2.855202 and f(x2) = 0.000101
Iteration-18, x2 = 2.855198 and f(x2) = 0.000027
Iteration-19, x2 = 2.855196 and f(x2) = -0.000011
Iteration-20, x2 = 2.855197 and f(x2) = 0.000008

Required Root is : 2.85519695
  1. Bisection Method Algorithm
  2. Bisection Method Pseudocode
  3. Python Program for Bisection Method
  4. C Program for Bisection Method
  5. C++ Program for Bisection Method
  6. MATLAB Program for Bisection Method
  7. Bisection Method Advantages
  8. Bisection Method Disadvantages
  9. Bisection Method Features
  10. Convergence of Bisection Method
  11. Bisection Method Online Calculator