{
  "abstract": "In this work, we introduce high-order Basis-Update & Galerkin (BUG) integrators based on explicit Runge-Kutta methods for large-scale matrix differential equations. These dynamical low-rank integrators extend the BUG integrator [1] to arbitrary explicit Runge-Kutta schemes by performing a BUG step at each stage of the method. The resulting Runge-Kutta BUG (RK-BUG) integrators are robust with respect to small singular values, fully forward in time, and high-order accurate, while enabling conservation and rank adaptivity. We prove that RK-BUG integrators retain the order of convergence of the underlying Runge-Kutta method until the error reaches a plateau corresponding to the low-rank truncation error, which vanishes as the rank becomes full. This theoretical analysis is supported by several numerical experiments. The results demonstrate the high-order convergence of the RK-BUG integrator and its superior accuracy compared to other existing dynamical low-rank integrators.",
  "abstract_shown": true,
  "affiliations": [
    "CSQI Chair, École Polytechnique Fédérale de Lausanne, Lausanne, 1015 Switzerland"
  ],
  "article_type": "research article",
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Fabio Nobile",
      "orcid": "0000-0002-8130-0114"
    },
    {
      "affs": [
        0
      ],
      "name": "Sébastien Riffaud",
      "orcid": "0009-0008-9133-5282"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2nkth6qhsm4xm.bib",
  "cited_by": 12,
  "doi": "10.1007/s10915-026-03317-5",
  "fulltext_url": "https://europepmc.org/articles/PMC13677646",
  "id": "2nkth6qhsm4xm",
  "issns": [
    "0885-7474",
    "1573-7691"
  ],
  "landing_url": "https://europepmc.org/article/MED/42898398",
  "language": "eng",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2612|Numerical Solvers for Ordinary Differential Equations"
    ],
    [
      "openalex",
      "2612|Numerical methods for differential equations"
    ]
  ],
  "openalex": "W7161075634",
  "pdf_url": "https://europepmc.org/articles/PMC13677646?pdf=render",
  "pmcid": "PMC13677646",
  "pmid": "42898398",
  "published": "2026-05-13",
  "publisher": "Springer Science+Business Media",
  "ris": "https://research.draconitic.com/paper/2nkth6qhsm4xm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:42Z",
      "native_id": "MED:42898398",
      "source": "europepmc",
      "url": "https://europepmc.org/article/MED/42898398"
    },
    {
      "first_seen": "2026-11-04T13:20:59Z",
      "native_id": "W7161075634",
      "source": "openalex",
      "url": "https://doi.org/10.1007/s10915-026-03317-5"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2612|Numerical Solvers for Ordinary Differential Equations",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "High-Order BUG Dynamical Low-Rank Integrators Based on Explicit Runge-Kutta Methods.",
  "title_text": "High-Order BUG Dynamical Low-Rank Integrators Based on Explicit Runge-Kutta Methods.",
  "type": "peer-reviewed",
  "updated_at": "2026-11-09T13:21:00Z",
  "url": "https://research.draconitic.com/paper/2nkth6qhsm4xm",
  "venue": "Journal of scientific computing",
  "versions": []
}