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'''
Cosine function is integrated by Euler and RK4 methods.
Results at each step is compared with sine function.
'''
from pylab import *
def rk4(x, y, fx, h = 0.1): # x, y , derivative, stepsize
k1 = h * fx(x)
k2 = h * fx(x + h/2.0)
k3 = h * fx(x + h/2.0)
k4 = h * fx(x + h)
return y + ( k1/6 + k2/3 + k3/3 + k4/6 )
h = 0.1 # stepsize
x = 0.0 # initail values
ye = 0.0 # for Euler
yr = 0.0 # for RK4
ax = [] # Lists to store calculated values
euerr = []
rkerr = []
while x < 2*pi:
ye = ye + h * math.cos(x) # Euler method
yr = rk4(x, yr, cos, h) # Runge-Kutta method
x = x + h
ax.append(x)
euerr.append(ye - sin(x))
rkerr.append(yr - sin(x))
plot(ax,euerr,'+')
plot(ax, rkerr,'ro')
show()
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