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'''
Sine function is calculated using its derivative, cosine.
Using Euler and RK4 method, with
'''
import math
def rk4(x, y, yprime, dx = 0.01): # x, y , derivative, stepsize
k1 = dx * yprime(x)
k2 = dx * yprime(x + dx/2.0)
k3 = dx * yprime(x + dx/2.0)
k4 = dx * yprime(x + dx)
return y + ( k1/6 + k2/3 + k3/3 + k4/6 )
h = 0.01 # stepsize
x = 0.0 # initail values
y = 0.0 # for Euler
z = 0.0 # for RK4
while x < math.pi:
print( x, y - math.sin(x), z - math.sin(x)) # errors
y = y + h * math.cos(x) # Euler method
z = rk4(x,z,math.cos,h) # Runge-Kutta method
x = x + h
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