# (c) Rory Clune 3/4/2011
# Euler method to solve SHM. Horrible performance!

from numpy import *

h = 0.0001
t = arange(0,100*pi,h)
y = [1,0]
ynew = [1,0]
error = 0
t=0
while (t<100*pi):    
	ynew[0] = y[0]+h*y[1]
	ynew[1] = y[1]-h*y[0]
	y[0] = ynew[0]
	y[1] = ynew[1]
	t+=h
	error+=fabs(cos(t)-y[0])
        
print "Euler Method with step size = " + str(h)
print "Average error = " + str(error/(int)(100*pi/h))
print "Final value error = " + str(cos(t)-y[0])