Date: Thu, 13 Dec 2001 12:39:32 +0100 From: Nils Wagner <nwagner@mecha.uni-stuttgart.de> Subject: [Numpy-discussion] Forth-Order Runge-Kutta

I am looking for an implementation of the fourth-order Runge-Kutta method in Numpy.

Here is one I wrote (based on a similar I had seen in lorentz.py in the PyOpenGL demos, I believe), that I used for chaotic dynamics visualizations. # A simple, non-stepsize adaptive fourth order Runge-Kutta integration # estimator method. def fourth_order_runge_kutta(self, xyz, dt): derivative = self.differentiator hdt = 0.5 * dt xyz = asarray(xyz) # Force tuple or list to an array k1 = array(derivative(xyz)) k2 = array(derivative(xyz + k1 * hdt)) k3 = array(derivative(xyz + k2 * hdt)) k4 = array(derivative(xyz + k3 * dt)) new_xyz = xyz + (k1 + k4) * (dt / 6.0) + (k2 + k3) * (dt / 3.0) return new_xyz where self.differentiator is a function that takes an x,y,z coordinate tuple, and returns the deriviative as an x,y,z coordinate tuple. I wrote this when I was much more naive about Runge-Kutta and Python Numeric, so don't use it without some looking over. It is at least a good starting point. -- Chad Netzer cnetzer@mail.arc.nasa.gov