import numpy as np
import matplotlib.pyplot as plt


n=float(2000)
h=10*np.pi/n

t=np.zeros(int(n))
x=np.zeros(int(n))
y=np.zeros(int(n))

x[0]=1
y[0]=2

#symplektisk euler
for i in range(int(n-1)):
    x[i+1]=x[i]+h*(-2*x[i]+y[i]+np.sin(t[i]))
    y[i+1]=y[i]+h*(x[i+1]-2*y[i])
    t[i+1]=t[i]+h

plt.plot(t,x)
plt.plot(t,y)
plt.show()

#plt.savefig('krets')