{
  "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.",
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  "article_type": null,
  "arxiv": "2609.29950",
  "author_total": 3,
  "authors": [
    {
      "name": "Charles-Édouard Bréhier"
    },
    {
      "name": "David Cohen"
    },
    {
      "name": "Gijs Custers"
    }
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  "bibtex": "https://research.draconitic.com/paper/2xr8zacjvph97.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.29950",
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  "id": "2xr8zacjvph97",
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  "language": "en",
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      "2612|Numerical methods for differential equations"
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  "pdf_url": "https://hal.science/hal-05764532/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2xr8zacjvph97.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:41Z",
      "native_id": "hal-05764532",
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      "url": "https://hal.science/hal-05764532v1"
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      "native_id": "2609.29950",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.29950"
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  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
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    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
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  ],
  "title": "Domain preserving splitting schemes for a class of SPDEs driven by a standard Brownian motion",
  "title_text": "Domain preserving splitting schemes for a class of SPDEs driven by a standard Brownian motion",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/2xr8zacjvph97",
  "venue": "HAL",
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}