Poisson's equation is the partial differential equation:

<math>

{\partial^2 \over \partial x^2 }\varphi(x,y,z) + {\partial^2 \over \partial y^2 }\varphi(x,y,z) + {\partial^2 \over \partial z^2 }\varphi(x,y,z) = f(x,y,z) <math>

Or alternately:

<math>{\nabla}^2 \varphi = f<math>

or

<math>\Delta\varphi=f,<math>

i.e., it sets the Laplacian equal to f.

Finding φ for some given f is an important practical problem, since this is the usual way to find the electric potential for a given charge distribution.

<math>{\nabla}^2 V = - {\rho \over \epsilon_0}<math>

There are various methods for numerical solution. The relaxation method, an iterative algorithm, is one example.

See also: Screened Poisson equation

fr:�quation de Poisson sl:Poissonova enačba