Nonlinear 1

import numpy as np
import matplotlib.pyplot as plt

#----------------

def bisection(f, a, b, tol=1E-4, maxit=10000):

    fa = f(a)
    fb = f(b)

    if fa==0: return a, 0
    if fb==0: return b, 0

    if fa*fb > 0.0:
        print("a, b don't bracket the root, try again")
        return np.nan, -1

    for k in range(1,maxit+1):

        c = 0.5*(a+b)
        fc = f(c)
        if fc==0: return c, k

        if np.abs(fc) <= tol or np.abs((b-a)/c) <= tol:
            return c, k

        if fa*fc <= 0: 
            b = c
            fb = fc
        else:
            a = c
            fa = fc

    print(f"no convergence in {maxit} iterations")
    return c, maxit

#----------------

def f(x): return (x-2.0)**2 - 1.0

x,k = bisection(f, 2.0, 100.0)

print(x,k)
print(f(x))

3.0000228881835938 18
4.577689105644822e-05