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Developments in dynamical systems theory provides new support for thediscretisation of \pde{}s and other microscale systems. Here we explore themethodology applied to the gap-tooth scheme in the equation-free approach ofKevrekidis in two spatial dimensions. The algebraic detail is enormous so wedetail computer algebra procedures to handle the enormity. However, modellingthe dynamics on 2D spatial patches appears to require a mixed numerical andalgebraic approach that is detailed in this report. Being based upon thecomputation of residuals, the procedures here may be simply adapted to a wideclass of reaction-diffusion equations.

Computer algebra derives the slow manifold of patch or element dynamics on lattices in two dimensions