one-file-projects/rk3.py

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#!/usr/bin/env python
import math
def rk3(h,tn,yn,ys,param=[]):
k1 = ys(tn,yn,*param)
k2 = ys(tn+h/2,yn+h*k1/2,*param)
k3 = ys(tn+h,yn - h*k1 + 2*h*k2, *param)
return tn+h, yn + h*(k1/3 + k2/3 + k3/3)
def main():
U = lambda tn,f : math.sin(2*math.pi*tn*f)
R = 5e3
C = 1e-6
us = lambda tn, un, f: (U(tn,f) - un)/(R*C)
fc = 1.0/(2*math.pi*R*C)
for f in [ 2**(i) * fc for i in range(-5,8)]:
ucmax = 0
ucmin = 0
tn = 0
un = 0
for i in range(1000000):
tn, un = rk3(0.000001, tn, un, us, [f])
ucmax = max(un,ucmax)
ucmin = min(un,ucmin)
print(" %10.3f : %10.6f %10.6f" % (f,ucmax,ucmin))
if __name__ == '__main__':
main()