  We present a convergence proof of the projective integration method for a
class of deterministic multi-dimensional multi-scale systems which are amenable
to centre manifold theory. The error is shown to contain contributions
associated with the numerical accuracy of the microsolver, the numerical
accuracy of the macrosolver and the distance from the centre manifold caused by
the combined effect of micro- and macrosolvers, respectively. We corroborate
our results by numerical simulations.
