The finite difference method is a method for solving partial
differential equations (PDEs). For example a PDE will involve
a function u(**x**) defined for all **x** in the domain
with respect to some given boundary condition. The purpose
of the method is to determine an approximation
to the function u(**x**).

The method requires the domain to be replaced by a grid. At each grid point each term in the partial differential is replaced by a difference formula which may include the values of u at that and neighbouring grid points. By substituting the difference formulae into the PDE, a difference equation is obtained.

In time-dependent PDEs, the FDM may be used in both space and time (as it is in the finite-difference time-domain (FD-TD) method in electromagnetics) or it may be used for the time component only, as is the case in the method of lines.