Exploring the behavior of asymptotic preserving schemes for a class of stochastic systems
Résumé
We consider a class of slow-fast stochastic systems, in the regime governed by the averaging principle. The fast component is a Brownian motion on a torus. We rst consider a system where the slow component solves an ordinary differential equation: we study a numerical scheme, which is shown to be asymptotic preserving and to satisfy uniform strong error estimates. Numerical experiments illustrate the results. We then provide numerical experiments for variants of the systems where the slow evolution is also driven by a Brownian motion. Finally, we propose and test a candidate higher-order method.
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