Communications in Mathematical Sciences

Volume 12 (2014)

Number 2

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

Pages: 235 – 255

DOI: https://dx.doi.org/10.4310/CMS.2014.v12.n2.a2

Authors

Georg A. Gottwald (School of Mathematics and Statistics, University of Sydney, Australia)

John MacLean (School of Mathematics and Statistics, University of Sydney, Australia)

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 center 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 center manifold caused by the combined effect of micro- and macrosolvers, respectively. We corroborate our results by numerical simulations.

Keywords

multi-scale integrators, projective integration, heterogeneous multiscale methods

2010 Mathematics Subject Classification

34-xx, 37Mxx, 65Pxx

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Published 20 September 2013