Bisection Method Example: Hand Solution and Python Code

Find the solution of the following equation using the bisection method:

Write a Python 3 code for this method.

Solution

Hand Solution

Let’s choose the initial values of x so that

have different signs:

Plugging the above values into the equation, we get:

The next value of x is:

Then we will plug the

   

value into the equation:

As the signs of

are the same, we will replace the x0 value with x2 and repeat the above steps:

Now, we will replace the x1 value with x2, as the signs of

are the same:

As

the root of the equation is approximately equal to 1.89282.

Python 3 Code

Let’s define a function for our equation first:

Now, we will write a function for defining the sign:

This is our main function for finding the root of the equation. As we must choose two initial values for x, our function should accept two initial parameters:

For simplification:

And let’s repeat the above steps in a while loop. In order to prevent infinite loop, it’s important to add an exit condition. In our case we will check if the absolute value of y is larger than the 0.001 threshold. To decide what x value should be replaced, the sign check statement will be written as follows:

At last, the found x value is returned:

The entire code:

The bisection method is one of the root-finding methods for continuous functions. If you want to become an expert at mathematics, you should carefully check our bisection method example and learn more about it.

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