maths.numerical_analysis.runge_kutta
====================================

.. py:module:: maths.numerical_analysis.runge_kutta


Functions
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.. autoapisummary::

   maths.numerical_analysis.runge_kutta.runge_kutta


Module Contents
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.. py:function:: runge_kutta(f, y0, x0, h, x_end)

   Calculate the numeric solution at each step to the ODE f(x, y) using RK4

   https://en.wikipedia.org/wiki/Runge-Kutta_methods

   Arguments:
   f -- The ode as a function of x and y
   y0 -- the initial value for y
   x0 -- the initial value for x
   h -- the stepsize
   x_end -- the end value for x

   >>> # the exact solution is math.exp(x)
   >>> def f(x, y):
   ...     return y
   >>> y0 = 1
   >>> y = runge_kutta(f, y0, 0.0, 0.01, 5)
   >>> float(y[-1])
   148.41315904125113