import numpy as np
import matplotlib.pyplot as plt
A    = 0.3   # The A constant in the ODE
t0   = 0.    # Starting time
tend = 10.   # End time
nt   = 10    # Nr of time steps
t    = np.linspace(t0,tend,nt)
y    = np.zeros(nt)
y[0] = 2.    # Intial condition
for it in range(0,nt-1):
   y[it+1] = y[it] - A * y[it] * ( t[it+1] - t[it] )
yana = y[0]*np.exp(-A*t)
plt.figure()
plt.plot(t,yana,label='Analytic')
plt.plot(t,y,'o',label='Numeric')
plt.xlabel('t')
plt.ylabel('y(t)')
plt.legend()
plt.savefig('fig_ode_euler_1_1.pdf')
plt.show()