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Task/Runge-Kutta-method/Python/runge-kutta-method.py

@@ -0,0 +1,21 @@
+def RK4(f):
+    return lambda t, y, dt: (
+            lambda dy1: (
+            lambda dy2: (
+            lambda dy3: (
+            lambda dy4: (dy1 + 2*dy2 + 2*dy3 + dy4)/6
+            )( dt * f( t + dt  , y + dy3   ) )
+	    )( dt * f( t + dt/2, y + dy2/2 ) )
+	    )( dt * f( t + dt/2, y + dy1/2 ) )
+	    )( dt * f( t       , y         ) )
+
+def theory(t): return (t**2 + 4)**2 /16
+
+from math import sqrt
+dy = RK4(lambda t, y: t*sqrt(y))
+
+t, y, dt = 0., 1., .1
+while t <= 10:
+    if abs(round(t) - t) < 1e-5:
+	print("y(%2.1f)\t= %4.6f \t error: %4.6g" % ( t, y, abs(y - theory(t))))
+    t, y = t + dt, y + dy( t, y, dt )