Work

Domain preserving splitting schemes for a class of SPDEs driven by a standard Brownian motion

Year: 2026

Type: preprint

Abstract: We consider a class of SPDEs driven by a standard real-valued Brownian motion, with drift and diffusion coefficients such that there exists a unique mild solution taking values in the interval $[-1,1]$ almost surely. To preserve this qualitative property of the exact solution, we propose a domain preserving Lie--Trotter splitting scheme: for any choice of the time-step size, the numerical solution takes values in the interval $[-1,1]$ almost surely. Furthermore, we prove mean-square convergence with rate $1/2-$ for the domain preserving Lie--Trotter scheme. These theoretical results are illustrated with numerical experiments.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.29950

Authors: Bréhier, Charles-Edouard, Cohen, David, Custers, Gijs

Institutions: Centre National de la Recherche Scientifique, Université de Pau et des Pays de l'Adour, Laboratoire de Mathématiques et de leurs Applications, Chalmers University of Technology, University of Gothenburg

Language: English

Topic: Numerical Solvers for Ordinary Differential Equations

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Chalmers Tekniska Högskola, Vetenskapsrådet

Award: NAISS

OpenAlex ID: W7214403608

Cites: 4

Cited by:

Related to: 10