maths.euler_method
==================

.. py:module:: maths.euler_method


Functions
---------

.. autoapisummary::

   maths.euler_method.explicit_euler


Module Contents
---------------

.. py:function:: explicit_euler(ode_func: collections.abc.Callable, y0: float, x0: float, step_size: float, x_end: float) -> numpy.ndarray

   Calculate numeric solution at each step to an ODE using Euler's Method

   For reference to Euler's method refer to https://en.wikipedia.org/wiki/Euler_method.

   Args:
       ode_func (Callable):  The ordinary differential equation
           as a function of x and y.
       y0 (float): The initial value for y.
       x0 (float): The initial value for x.
       step_size (float): The increment value for x.
       x_end (float): The final value of x to be calculated.

   Returns:
       np.ndarray: Solution of y for every step in x.

   >>> # the exact solution is math.exp(x)
   >>> def f(x, y):
   ...     return y
   >>> y0 = 1
   >>> y = explicit_euler(f, y0, 0.0, 0.01, 5)
   >>> float(y[-1])
   144.77277243257308