import numpy as np
import matplotlib.pyplot as plt

t_final = 10.0
h = 0.1
t_vec = np.arange(0.0, t_final/h) * h
t_steps = len(t_vec) - 1

# print the times
print t_vec

x0 = 1.0
y0 = 0.0
a = 1.0
b = 0.5

x = x0
y = y0
x_vec = np.zeros((t_steps + 1,))
y_vec = np.zeros((t_steps + 1,))
x_vec[0]=x
y_vec[0]=y
for k in range(t_steps):


    x_vec[k+1] = x_vec[k] + h * (-a * x_vec[k])
    y_vec[k+1] = y_vec[k] + h * (a * x_vec[k] - b * y_vec[k])

    
#    x = x_vec[k]
#    y = y_vec[k]
#    
#    x_new = x + h *( -a * x)
#    y_new = y + h *( a * x - b * y)
#
#    x = x_new
#    y = y_new
#    x_vec[k+1] = x
#    y_vec[k+1] = y


    
    #print x, y


fig = plt.figure()
plt.plot(t_vec, x_vec)
plt.plot(t_vec, y_vec)
plt.legend(['x(t)', 'y(t)'])
plt.xlabel('tid')


plt.show()