Consider the following *one-step* explicit difference scheme, which relates values of the grid function
to values at the previous time step:

where is some subset of , and the parameters are constants; it is initialized by setting equal to some function (assumed to be in ). Taking the spatial Fourier transform of this recursion gives

so defined is called the

where is the spatial Fourier transform of the initial condition . (A.3) further implies that

and finally, through Parseval's relation, that

If the which define the difference scheme are independent of the grid spacing and the time step, then such a difference scheme is called

The norm of the solution to the difference equation will thus not increase as the simulation progresses.