{
  "abstract": "Hyperbolic PDEs with time delay are essential for modeling a wide range of real-world applications. Since closed-form solutions are often not attainable, developing accurate and efficient numerical methods becomes crucial. In this work a novel substructuring waveform relaxation method namely Neumann-Neumann Waveform Relaxation (NNWR) has been implemented for numerically solving hyperbolic delay PDEs in the case of non-uniform subdomain partitioning. The convergence behavior is first analyzed using Fourier analysis to obtain an estimate, followed by a demonstration of finite-step convergence through Laplace transform techniques. Various test cases are presented as numerical illustrations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.11098",
  "author_total": 1,
  "authors": [
    {
      "name": "Deeksha Tomer"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/003jwtcs50za4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11098",
  "fulltext_url": null,
  "id": "003jwtcs50za4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.11098",
  "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.AP"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "2206|Advanced Numerical Methods in Computational Mathematics"
    ]
  ],
  "openalex": "W7212305222",
  "pdf_url": "https://arxiv.org/pdf/2609.11098",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/003jwtcs50za4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.11098",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11098"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Neumann-Neumann Waveform Relaxation Method for Hyperbolic PDE with Time Delay",
  "title_text": "Neumann-Neumann Waveform Relaxation Method for Hyperbolic PDE with Time Delay",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/003jwtcs50za4",
  "venue": "arXiv",
  "versions": []
}