Poisson's equation
Poisson's equation is the
differential equation:
-
Or alternately:
or
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.
There are various methods for numerical solution. The
relaxation method, an iterative algorithm, is one example.