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'''
Solving initial value problem using 4th order Runge-Kutta method.
Sine function is calculated by integrating its derivative, cosine.
'''
from pylab import *
def rk4(x, y, fx, h = 0.01): # 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 = 0.01 # stepsize
x = 0.0 # initail values
y = 0.0
ax = [x]
ay = [y]
while x < math.pi:
y = rk4(x,y,math.cos) # Runge-Kutta method
x = x + h
ax.append(x)
ay.append(y)
plot(ax,ay)
show()
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