normal_ode

normal_ode, an Octave 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)

        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.

The information on this web page is distributed under the MIT license.

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

octave_ode, an Octave code which sets up various ordinary differential equations (ODE).

euler.m, solves an ordinary differential equation (ODE) using the Euler method.
normal_deriv.m, returns the right hand side of an ODE that defines the normal PDF.
normal_solution.m, returns value of the normal PDF.
rms.m, returns the root mean square (RMS) norm of a vector.
timestamp.m, prints the YMDHMS date as a timestamp.

Last revised on 12 October 2020.