{
  "annotation_id": "9bf6f6c1-e5b8-4fad-a135-bb659dd4ffa9",
  "date_created": "2026-03-02T18:01:21.886000Z",
  "date_modified": "2026-03-02T18:01:21.886000Z",
  "file_hash": "0cc9be4a25dd99fef75f3416f1dd2487d85ee6b0b0e602528aa25b1ce8cbd71e",
  "private": false,
  "record": {
    "abstract": "We present numerical solutions for differential equations by expanding the\nunknown function in terms of Chebyshev polynomials and solving a system of\nlinear equations directly for the values of the function at the extrema (or\nzeros) of the Chebyshev polynomial of order N (El-gendi\u0027s method). The\nsolutions are exact at these points, apart from round-off computer errors and\nthe convergence of other numerical methods used in connection to solving the\nlinear system of equations. Applications to initial value problems in\ntime-dependent quantum field theory, and second order boundary value problems\nin fluid dynamics are presented.",
    "arxiv_id": "physics/9901005",
    "authors": [
      "Bogdan Mihaila",
      "Ioana Mihaila"
    ],
    "categories": [
      "physics.comp-ph",
      "hep-ph"
    ],
    "doi": "10.1088/0305-4470/35/3/317",
    "journal_ref": "J. Phys. A: Math. Gen. 35, 731 (2002)",
    "title": "Numerical Approximations Using Chebyshev Polynomial Expansions",
    "url": "https://arxiv.org/abs/physics/9901005"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "007a6877-dfff-44b7-b2c5-84dfaf943bc2",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}