import math

import matplotlib.pyplot as plt

import numpy as np

def logistic (t):

return 1000./(1+999*math.exp(-2*t))

x = np.linspace(0,10,11)

y = [logistic(i) for i in x]

plt.scatter(x,y)

plt.plot(x, y)

def ode_FE(f, U_0, dt, T):

return u, t

for dt, T in zip((0.5, 20), (60, 100)):

u, t = ode_FE(f=lambda u, t: 0.1*(1 - u/500.)*u, \

U_0=100, dt=dt, T=T)

plt.figure() # Make separate figures for each pass in the loop

plt.plot(t, u, 'b-')

plt.xlabel('t'); plt.ylabel('N(t)')

plt.savefig('tmp_%g.png' % dt); plt.savefig('tmp_%g.pdf' % dt)