PreprintCC BY 4.0arXiv
Overcoming the spatial order barrier for nonlinear SPDEs with additive space-time white noise
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.
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BibTeX
@misc{anzeletti2026overcoming,
title = {{Overcoming the spatial order barrier for nonlinear SPDEs with additive space-time white noise}},
author = {Lukas Anzeletti and Máté Gerencsér and Helena Kremp},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.28727},
eprint = {2608.28727},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.28727},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Overcoming the spatial order barrier for nonlinear SPDEs with additive space-time white noise
AU - Lukas Anzeletti
AU - Máté Gerencsér
AU - Helena Kremp
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2608.28727
UR - https://arxiv.org/abs/2608.28727
AB - 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.
ER -