| Abstract: |
| We study a time-space discretization scheme for the non-linear stochastic heat equation driven by space-time white noise, with a singular reaction term b modeled as a distribution. Our numerical procedure combines a finite difference method in space with an Euler scheme, together with a taming of the singular reaction term. Under suitable scaling of all numerical parameters, we obtain strong convergence results with explicit rate that allow not only the visualization of trajectories but also the exploration of long-time statistical properties.
In particular, we will focus on the approximation of the invariant measure associated with the equation. By combining dissipative Lipschitz drift with a singular drift of small Besov norm, we can study the long-time behavior and provide numerical schemes that capture the invariant distribution.
This is joint work with Charles-Edouard Brehier, El Mehdi Haress, Jonathan Naffrichoux, and Alexandre Richard |
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