Overcoming the spatial order barrier for nonlinear SPDEs with additive space-time white noise
Year: 2026
Type: preprint
Abstract: We introduce a fully discrete numerical scheme for semilinear SPDEs with additive space-time white noise that overcomes the previous order barrier for the spatial convergence rate. The scheme, which we refer to as the doubly accelerated exponential Euler scheme, achieves a strong convergence rate of $M^{-1+ε}$ in time and $N^{-3/2+ε}$ in space for any $ε>0$, where $M^{-1}$ and $N^{-1}$ are the temporal, respectively the spatial, meshsizes. This substantially improves the standard spatial error bounds of order $N^{-1/2}$ in the literature. Numerical simulations support the findings.
Source: arXiv (Cornell University)
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204952267