The bisection method is one of the implicit methods used to find roots. An attempt is made to find the root with a lower and upper value containing the root. If the value of a function changes from - to + or from + to -, then that function value becomes zero at some point in this transition.
We perform the root of the equation 𝑥**3 − 2*(x**2) − 5 = 0 in the interval [2,4] with the method in 4 iterations.
x**3 +4*(x**2)-10=0 in the interval [1,2] until the margin of error relative to the solution is ε = 10**-6 by the method of dividing the root by two we will continue.
-Let's define a function for the equation.
-Next, let's define the function of the Bisection method and code the algorithm of the Bisection method.
-Then let's get the "lower range", "upper range" and "number of iterations" values from the user.
-But there is one thing we should be careful about: the product of the value of the function in the lower range and the value of the function in the upper range must be less than 0!
-If it is less than zero, we can call the function.
If we talk about the algorithm of the bisection method:
-First we define an i variable value. This i value will be important for the loop we will use later.
-Then we define an x value and this x value will hold the value of (upper + lower)/2 in the bisection method. We set the value 0 at the beginning.
-We set the loop and x We update xi as =(lower range+upper range)/2.
-If the value of x in the function is less than zero, lower bound=x, otherwise upper bound=x.
-Then i for the loop to continue We increase its value.
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