#
# Explicit Euler method
# Vincent Legat - 2018
# Ecole Polytechnique de Louvain
#
from numpy import *
from matplotlib import pyplot as plt
Xstart = 0; Xend = 3; Ustart = 1;
for n in [3,6,12,24]:
h = (Xend-Xstart)/n
X = linspace(Xstart,Xend,n+1)
U = zeros(n+1); U[0] = Ustart
for i in range(n):
U[i+1] = U[i] + h*(X[i]-U[i])/2
plt.plot(X,U,'.-b')
plt.show()