lines 6-43 of file: python/xam/runge_kutta.py

{xrst_begin xam_runge_kutta.py}

Example and Test of Python runge_kutta
######################################

ODE
***

.. math::

   y_i '(t) & = 0           \; & \mbox{for} \; i = 0 \\
   y_i '(t) & = y_{i-1} (t) \; & \mbox{for} \; i > 0

Initial Value
*************

.. math::

   y_i (0) & = 1   \; & \mbox{for} \; i = 0 \\
   y_i (0) & = 0   \; & \mbox{for} \; i > 0 \\

Solution
********

.. math::

   y_0 (t) & = 1               \\
   y_1 (t) & = t               \\
   y_i (t) & = t^i / i !       \\

Source Code
***********
{xrst_literal
   # BEGIN PYTHON
   # END PYTHON
}

{xrst_end xam_runge_kutta.py}