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We present a convergence proof of the projective integration method for aclass of deterministic multi-dimensional multi-scale systems which are amenableto centre manifold theory. The error is shown to contain contributionsassociated with the numerical accuracy of the microsolver, the numericalaccuracy of the macrosolver and the distance from the centre manifold caused bythe combined effect of micro- and macrosolvers, respectively. We corroborateour results by numerical simulations.

On convergence of the projective integration method for stiff ordinary differential equations