# -*- coding: utf-8 -*-
"""
Created on Fri Mar 25 14:23:19 2022

@author: turinici
"""

import numpy as np
import matplotlib.pyplot as plt

np.sqrt(2)**2 - 1 
#np.sqrt(2)*np.sqrt(2) - 1

T=1.0
N=100
h = T/N

U0exact=0.0
U0=np.sqrt(2)**2 - 2

Uexact = np.zeros(N+1)
Uexact[0]=U0exact

U = np.zeros(N+1)
U[0]=U0

#implementation Euler Explicite
for k in range(N):
    U[k+1]=U[k]+h*2*np.sqrt(np.abs(U[k]))
    Uexact[k+1]=Uexact[k]+h*2*np.sqrt(np.abs(Uexact[k]))

plt.figure(1)
plt.plot(np.linspace(0,T,N+1),U,
         np.linspace(0,T,N+1),Uexact)
plt.legend(['precision finie','precision infinie'])