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

2013/01/29 by Maclean, John, Gottwald, Georg A. · 1 citation
#Chaotic Dynamics (nlin.CD) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1301.6851

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.

Cited by

• Generalised projective integration scheme in equation-free multiscale modelling

Related

• On convergence of higher order schemes for the projective integration method for stiff ordinary differential equations
• Projective Integration Methods in the Runge-Kutta Framework and the Extension to Adaptivity in Time
• Analysis of multiscale methods for stochastic dynamical systems driven by α-stable processes
• A micro-macro parareal algorithm: application to singularly perturbed ordinary differential equations
• Macroscale, slowly varying, models emerge from the microscale dynamics in long thin domains