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

TL;DR

This paper proves the convergence of the projective integration method for certain multi-scale stiff ODEs, analyzing error sources and validating results through numerical simulations.

Contribution

It provides a rigorous convergence proof for the projective integration method applied to multi-scale systems using centre manifold theory.

Findings

Error contributions from microsolver and macrosolver are characterized.

Convergence is validated through numerical simulations.

The method effectively handles multi-scale stiff ODEs.

Abstract

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.