Article ID Journal Published Year Pages File Type
4642180 Journal of Computational and Applied Mathematics 2008 20 Pages PDF
Abstract

In the context of multiscale computations, techniques have recently been developed that enable microscopic simulators to perform macroscopic level tasks (equation-free multiscale computations). The main tool is the so-called coarse-grained time-stepper, which implements an approximation of the unavailable macroscopic time-stepper using only the microscopic simulator. Several schemes were developed to accelerate the coarse-grained time-stepper, exploiting the smoothness in time of the macroscopic dynamics. To date, mainly the stability of these methods was analyzed. In this paper, we focus on their accuracy properties, mainly in the context of parabolic problems. We study the global error of the different methods, compare with explicit stiff ODE solvers, and use the theoretical results to develop more accurate variants. Our theoretical results are confirmed by various numerical experiments.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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