Root Finding Techniques | Bisection Method

In this article, we will be going to study the bisection method in numerical analysis and design using Python.

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Algorithm

• Read a,b,E

• i=0

• if f(a)*f(b)>0 the begin write 'starting values unsuitable'

• endif

• while |f(m)|<0 do

• begin

• m=(a+b)/2

• i=i+1

• if f(a)*f(b)>0 then a=m else b=m

• endif

• write 'Solution converges to a root'

• write 'Number of iterations=',I

• write m,f(m)

• stop

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Flowchart

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Example

Q] Find the real root of equation x*x-x-1=0 by bisection method up to 4 decimal places? a and b are given as 1 and 2.

Solution-

import math

def f(x): 
    return x*x - x -1
   

def bisection(a,b): 
  
    if (f(a) * f(b) >= 0.0): 
        print("Invalid Interval\n") 
        return
   
    m=(a+b)/2
    while (abs(f(m))>= 0.01): 
  
        
        m= (a+b)/2
        if(f(m)==0.0):
            break

        if (f(m)*f(a) < 0.0): 
            b = m
        else: 
            a = m
              
    print("The value of root is : ","%.4f"%m) 
      

a =1.0
b = 2.0
bisection(a, b) 

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Happy Coding!

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