From 5fbf3ae49ca26b4bb02616d09132dbb4e53913d6 Mon Sep 17 00:00:00 2001
From: Valentin Gehrke <madmaurice@zom.bi>
Date: Thu, 18 Feb 2016 14:59:01 +0100
Subject: [PATCH] Lowpass simulation with runge kutte 3rd order

---
 rk3.py | 30 ++++++++++++++++++++++++++++++
 1 file changed, 30 insertions(+)
 create mode 100644 rk3.py

diff --git a/rk3.py b/rk3.py
new file mode 100644
index 0000000..5b6201a
--- /dev/null
+++ b/rk3.py
@@ -0,0 +1,30 @@
+#!/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()