| Abstract: |
| The numerical schemes for the approximation of stochastic partial differential equations rely on classical temporal schemes for stochastic differential equations. In the case of stochastic partial differential equations, time and space discretizations must be considered to obtain a fully discretized scheme. Moreover the statistical effects/errors cannot be neglected by naive numerical implementations. The weak convergence rates are usually better than strong orders, but the statistical errors are worse.
In this talk, I will present implementations of schemes for stochastic partial differential equations, in the case of non-globally Lipschitz non-linearities, with theoretical proofs of the weak and strong convergence rates. Moreover I will present numerical simulations to illustrate that these orders seem sharp in some chosen cases like Allen-Cahn equation, and the importance of the spatial discretization and the treatment of statistical errors. |
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