{
  "abstract": "Dynamical low-rank approximation has become a widely used numerical method in diverse disciplines. Its main idea is to represent the matrix or tensor-valued solution to a time-dependent differential equation as a low-rank factorization. The evolution of the factorization leads to highly stiff dynamics and requires the derivation of novel time integration methods that are not prone to this stiffness. A promising family of integrators are basis-update \\& Galerkin (BUG) integrators as they enable implicit time integration and structure--preservation. However, current BUG integrators are limited to second--order accuracy while general-order BUG integrators are designed as projections of explicit time integration methods, thus severely limiting their use. In this work, we propose general-order BUG integrators that do not rely on an explicit time integration scheme while requiring a smaller number of basis functions to achieve high-order accuracy. We prove a general order error bound for the proposed augmented and parallel BUG integrators and demonstrate their behaviour for a series of stiff and non-stiff numerical benchmarks in which they significantly outperform previous BUG versions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.27749",
  "author_total": 3,
  "authors": [
    {
      "name": "Cory D. Hauck"
    },
    {
      "name": "Jonas Kusch"
    },
    {
      "name": "Steffen Schotthöfer"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3mc16r5n1e47z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.27749",
  "fulltext_url": null,
  "id": "3mc16r5n1e47z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.27749",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "2612|Numerical methods for differential equations"
    ]
  ],
  "openalex": "W7204828537",
  "pdf_url": "https://arxiv.org/pdf/2608.27749",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3mc16r5n1e47z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:28Z",
      "native_id": "2608.27749",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.27749"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "High-order robust basis-update & Galerkin integrators for dynamical low-rank approximation",
  "title_text": "High-order robust basis-update & Galerkin integrators for dynamical low-rank approximation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:28Z",
  "url": "https://research.draconitic.com/paper/3mc16r5n1e47z",
  "venue": "arXiv",
  "versions": []
}