{
  "annotation_id": "8aeea5e3-d70c-4123-a2b2-e80790d168e8",
  "date_created": "2026-03-02T18:01:00.645000Z",
  "date_modified": "2026-03-02T18:01:00.645000Z",
  "file_hash": "bfca1f5572814762fa56d0999116bdb5b001d7d98de31e57b6d06edea15688c9",
  "private": false,
  "record": {
    "abstract": "We show that any second order linear ordinary diffrential equation with\nconstant coefficients (including the damped and undumped harmonic oscillator\nequation) admits an exact discretization, i.e., there exists a difference\nequation whose solutions exactly coincide with solutions of the corresponding\ndifferential equation evaluated at a discrete sequence of points (a lattice).\nSuch exact discretization is found for an arbitrary lattice spacing.",
    "arxiv_id": "physics/0507182",
    "authors": [
      "Jan L. Cieslinski",
      "Boguslaw Ratkiewicz"
    ],
    "categories": [
      "physics.pop-ph",
      "physics.comp-ph"
    ],
    "title": "On simulations of the classical harmonic oscillator equation by   difference equations",
    "url": "https://arxiv.org/abs/physics/0507182"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "0a446376-e2bd-435e-9776-4185107dea5c",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}