  I previously used Burgers' equation to introduce a new method of numerical
discretisation of \pde{}s. The analysis is based upon centre manifold theory so
we are assured that the discretisation accurately models all the processes and
their subgrid scale interactions. Here I show how boundaries to the physical
domain may be naturally incorporated into the numerical modelling of Burgers'
equation. We investigate Neumann and Dirichlet boundary conditions. As well as
modelling the nonlinear advection, the method naturally derives symmetric
matrices with constant bandwidth to correspond to the self-adjoint diffusion
operator. The techniques developed here may be used to accurately model the
nonlinear evolution of quite general spatio-temporal dynamical systems on
bounded domains.
