Partial differential equation

The Navier–Stokes differential equation, used to model airflow around an obstruction.

A Partial differential equation is a type of differential equation which relates a multivariable function to its partial derivatives. They are very commonly used in engineering and physics.

Examples

• $\frac{\part U}{\part x}+\frac{\part U}{\part y}+U=0$
• $\frac{\part^2U}{\part x^2}+\frac{\part U}{\part x}+xU=\frac{\part U}{\part y}$
• $\frac{\part^2U}{\part x^2}+\frac{\part^2U}{\part y^2}=xy$

The Diffusion Equation

$\frac{\partial u}{\partial t} = \alpha \bigtriangledown^2 u$

The Laplace Equation

$\bigtriangledown^2 u =0$

The Wave Equation

$\frac{\partial^2 u}{\partial t^2} = \alpha \bigtriangledown^2 u$