  I introduce an innovative methodology for deriving numerical models of
systems of partial differential equations which exhibit the evolution of
spatial patterns. The new approach directly produces a discretisation for the
evolution of the pattern amplitude, has the rigorous support of centre manifold
theory at finite grid size $h$, and naturally incorporates physical boundaries.
The results presented here for the Swift-Hohenberg equation suggest the
approach will form a powerful method in computationally exploring pattern
selection in general. With the aid of computer algebra, the techniques may be
applied to a wide variety of equations to derive numerical models that
accurately and stably capture the dynamics including the influence of possibly
forced boundaries.
