py_runge_kutta¶

Python Fourth Order Runge Kutta Method¶

Prototype¶

def runge_kutta(like_numpy, fun, yi, tf, ns) :
   assert type(ns) == int
   assert type(yi) == type( like_numpy.array(1.0) )
   return yf

Purpose¶

This routine returns an approximate solution for \(y( t^f )\) where \(y(0) = y^i\) and \(y' (t) = f(y)\) .

like_numpy¶

This is a like_numpy class. It is used to vectorize the rk4_step algorithm.

fun¶

This is a py_fun_obj . The syntax dy = fun ( yt ) , were yt is \(y(t)\) , sets dy equal to the derivative \(y'(t)\) .

yi¶

is the value of \(y(t)\) at \(t = 0\) . This is a vector like object with elements of type float or Scalar .

tf¶

is the value of t at which we wish to evaluate \(y(t)\) . This is an object of type float or Scalar .

ns¶

is the number of Runge-Kutta steps to use. The more steps the smaller the step size and the more accurate the solution. This is an int .

yf¶

The return value yf has the same size as yi and is the approximation for \(y(t)\) at t = tf . This is a vector like object with elements of type float or Scalar .

Source Code¶

runge_kutta.py

Example¶

xam_runge_kutta.py contains an example and test of py_runge_kutta .