{
  "annotation_id": "dbccdcf3-7dad-4968-a130-70b517a3ca4d",
  "date_created": "2026-02-17T05:53:23.491000Z",
  "date_modified": "2026-02-17T05:53:23.491000Z",
  "file_hash": "b00df26ac082b24e5588b542fad9f19849b028944ef9e6d67e4c0dc740ebe721",
  "private": false,
  "record": {
    "abstract": "This paper proposes specular differentiation in one-dimensional Euclidean space and provides its fundamental analysis, including quasi-Fermat\u0027s theorem and the quasi-Mean Value Theorem. As an application, this paper develops several numerical schemes for solving initial value problems for first-order ordinary differential equations. Based on numerical simulations, we select one scheme and prove its first-order consistency and second-order local convergence.",
    "arxiv_id": "2601.09900",
    "authors": [
      "Kiyuob Jung"
    ],
    "categories": [
      "math.NA",
      "cs.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Nonlinear numerical schemes using specular differentiation for initial value problems of first-order ordinary differential equations",
    "url": "https://arxiv.org/abs/2601.09900",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "8d71b129-3c0d-4ae2-a96d-f6bc7f69f150",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}