The equation-free framework for multiscale computing is built around the central idea of a coarse time-stepper, which is an approximate time integrator for the unavailable macroscopic model when only a microscopic simulator is given. In this paper, we study the numerical properties of the coarse time-stepper when a lattice Boltzmann model for one-dimensional diffusion is used as the microscopic simulator. We derive analytical expressions for the accuracy and stability of the coarse time-stepper, which allow us to study the influence of various aspects involved in its construction.
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