ANALYSIS OF SOME SPLITTING SCHEMES FOR THE STOCHASTIC ALLEN-CAHN EQUATION
Résumé
We introduce and analyze an explicit time discretization scheme for the one-dimensional stochastic Allen-Cahn, driven by space-time white noise. The scheme is based on a splitting strategy, and uses the exact solution for the nonlinear term contribution. We first prove boundedness of moments of the numerical solution. We then prove strong convergence results: first, L^2 (Ω)-convergence of order almost 1/4, localized on an event of arbitrarily large probability, then convergence in probability of order almost 1/4. The theoretical analysis is supported by numerical experiments, concerning strong and weak orders of convergence.
| Origine | Fichiers produits par l'(les) auteur(s) |
|---|
Loading...