| Abstract: |
| Constructing efficient methods for multiscale problems requires a lot of care. I will discuss the case of SDE systems, with unknowns $X^\epsilon$ and $\zeta^\epsilon$, depending on a small parameter $\epsilon$, where $\zeta^\epsilon$ is an Ornstein-Uhlenbeck process, such that $X^\epsilon$ converges in distribution to the solution of an SDE driven by a Wiener noise (typically interpreted in Stratonovich sense). It is desirable to construct asymptotic preserving schemes: for any fixed time-step size, there exists a limiting numerical scheme when $\epsilon$ goes to $0$, which is consistent with the limiting SDE. There is a huge literature on this topic for PDE models, but for stochastic systems there are only few results.
I will present new asymptotic preserving schemes for different classes of SDEs, study their properties (with theoretical and numerical results), and I will present an extension for some Stochastic kinetic linear PDEs. |
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