| Issue |
ESAIM: M2AN
Volume 58, Number 4, July-August 2024
|
|
|---|---|---|
| Page(s) | 1317 - 1346 | |
| DOI | https://doi.org/10.1051/m2an/2024032 | |
| Published online | 30 July 2024 | |
Analysis of a positivity-preserving splitting scheme for some semilinear stochastic heat equations
1
Universite de Pau et des Pays de l’Adour, E2S UPPA, CNRS, LMAP, Pau, France
2
Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, 41296 Gothenburg, Sweden
* Corresponding author: charles-edouard.brehier@univ-pau.fr
Received:
2
March
2023
Accepted:
29
April
2024
We construct a positivity-preserving Lie–Trotter splitting scheme with finite difference discretization in space for approximating the solutions to a class of semilinear stochastic heat equations with multiplicative space-time white noise. We prove that this explicit numerical scheme converges in the mean-square sense, with rate 1/4 in time and rate 1/2 in space, under appropriate CFL conditions. Numerical experiments illustrate the superiority of the proposed numerical scheme compared with standard numerical methods which do not preserve positivity.
Mathematics Subject Classification: 60H35 / 60M15 / 65J08
Key words: Stochastic partial differential equations / stochastic heat equation / splitting scheme / positivity-preserving scheme / mean-square convergence
© The authors. Published by EDP Sciences, SMAI 2024
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