{
  "abstract": "Parareal is a parallel-in-time method for initial-value problems that has found extensive applications and given rise to many variants. Krylov-enhanced parareal is a variant of parareal that uses projection techniques to accelerate convergence substantially for linear problems. In this paper, we study a projection-based parareal algorithm for nonlinear initial-value problems with a modified iteration scheme and an arbitrary orthogonal projection. For a general nonlinear problem, we prove a convergence estimate for each iteration step on a fixed time grid. We analyze the errors of the modified scheme and the scheme of Krylov-enhanced parareal relative to the old error as the coarse grid is refined. For a coarse solver of order $p$ and step size $h$, we prove error bounds of $O(h^{p+1})$ for the modified scheme and $O(h)$ for that of Krylov-enhanced parareal at the first potentially inexact time point under mild assumptions. Numerical experiments on two nonlinear problems are consistent with the theoretical analysis.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.21680",
  "author_total": 4,
  "authors": [
    {
      "name": "Chenyi Tan"
    },
    {
      "name": "Yuncheng Xu"
    },
    {
      "name": "Yehao Zhang"
    },
    {
      "name": "Yangfeng Su"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e4gbcqmc52q75.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21680",
  "fulltext_url": null,
  "id": "e4gbcqmc52q75",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.21680",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "2612|Numerical methods for differential equations"
    ]
  ],
  "openalex": "W7222669403",
  "pdf_url": "https://arxiv.org/pdf/2610.21680",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e4gbcqmc52q75.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.21680",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21680"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Projection-Based Parareal for Nonlinear Initial-Value Problems",
  "title_text": "Projection-Based Parareal for Nonlinear Initial-Value Problems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/e4gbcqmc52q75",
  "venue": "arXiv",
  "versions": []
}