maths.numerical_analysis.runge_kutta_gills
==========================================

.. py:module:: maths.numerical_analysis.runge_kutta_gills

.. autoapi-nested-parse::

   Use the Runge-Kutta-Gill's method of order 4 to solve Ordinary Differential Equations.

   https://www.geeksforgeeks.org/gills-4th-order-method-to-solve-differential-equations/
   Author : Ravi Kumar



Functions
---------

.. autoapisummary::

   maths.numerical_analysis.runge_kutta_gills.runge_kutta_gills


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

.. py:function:: runge_kutta_gills(func: collections.abc.Callable[[float, float], float], x_initial: float, y_initial: float, step_size: float, x_final: float) -> numpy.ndarray

   Solve an Ordinary Differential Equations using Runge-Kutta-Gills Method of order 4.

   args:
   func: An ordinary differential equation (ODE) as function of x and y.
   x_initial: The initial value of x.
   y_initial: The initial value of y.
   step_size: The increment value of x.
   x_final: The final value of x.

   Returns:
       Solution of y at each nodal point

   >>> def f(x, y):
   ...     return (x-y)/2
   >>> y = runge_kutta_gills(f, 0, 3, 0.2, 5)
   >>> float(y[-1])
   3.4104259225717537

   >>> def f(x,y):
   ...     return x
   >>> y = runge_kutta_gills(f, -1, 0, 0.2, 0)
   >>> y
   array([ 0.  , -0.18, -0.32, -0.42, -0.48, -0.5 ])

   >>> def f(x, y):
   ...     return x + y
   >>> y = runge_kutta_gills(f, 0, 0, 0.2, -1)
   Traceback (most recent call last):
       ...
   ValueError: The final value of x must be greater than initial value of x.

   >>> def f(x, y):
   ...     return x
   >>> y = runge_kutta_gills(f, -1, 0, -0.2, 0)
   Traceback (most recent call last):
       ...
   ValueError: Step size must be positive.