{
  "abstract": "This paper presents a numerical investigation of soft-to-hard terminal constraint convergence for optimal control problems governed by a second-order ordinary differential equation and the one-dimensional heat equation. The study complements the analytical convergence theory through comparisons with exact solutions and independently computed numerical approximations. For the heat equation, a fully discrete Crank--Nicolson finite-difference formulation is validated against exact modal solutions, exhibiting approximately second-order convergence in the terminal-state and midpoint-sampled control errors under simultaneous space-time mesh refinement. Numerical experiments demonstrate the predicted first-order penalty convergence for benchmark problems and investigate the admissibility threshold governing finite-energy exact terminal controllability. Additional modal experiments examine the dependence of terminal-error convergence rates on spectral regularity, illustrating intermediate rates consistent with the theoretical estimates and asymptotic predictions. The results provide computational evidence supporting the soft-to-hard convergence framework and clarify the roles of discretization, target admissibility, and spectral regularity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40461",
  "author_total": 2,
  "authors": [
    {
      "name": "Sung-Sik Kwon"
    },
    {
      "name": "Marcus Nunda"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6sscr25ggc5ez.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40461",
  "fulltext_url": null,
  "id": "6sscr25ggc5ez",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40461",
  "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"
    ],
    [
      "arxiv",
      "math.OC"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.40461",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6sscr25ggc5ez.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:35Z",
      "native_id": "2610.40461",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40461"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Numerical Investigation of Soft-to-Hard Convergence: Discretization, Admissibility, and Spectral Regularity",
  "title_text": "Numerical Investigation of Soft-to-Hard Convergence: Discretization, Admissibility, and Spectral Regularity",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:53Z",
  "url": "https://research.draconitic.com/paper/6sscr25ggc5ez",
  "venue": "arXiv",
  "versions": []
}