Communications in Mathematical Sciences
Volume 12 (2014)
On convergence of the projective integration method for stiff ordinary differential equations
Pages: 235 – 255
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.
multi-scale integrators, projective integration, heterogeneous multiscale methods
2010 Mathematics Subject Classification
34-xx, 37Mxx, 65Pxx