normal_ode


normal_ode, a Python code which describes an ordinary differential equation (ODE) for the normal probability density function (PDF).

The normal probability density function (PDF) can be written as

        y(t) = 1/sqrt(2 pi) e^(-t^2/2)
      
The derivative of the normal PDF is
        y'(t) = -t/sqrt(2 pi) e^(-t^2/2) = - t * y(t)
      

Thus, along with an initial condition, an ODE for the normal PDF can be written either as:

        y'(t) = -t/sqrt(2 pi) e^(-t^2/2)
      
or
        y'(t) = -t * y(t)
      
While both of these ODE's have the same solution, an ODE solver will generally have more difficulty solving the second version.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

normal_ode is available in a MATLAB version and an Octave version and a Python version.

Related Data and codes:

python_ode, Python codes which sets up various systems of ordinary differential equations (ODE).

Source Code:


Last revised on 30 October 2020.