{
  "annotation_id": "a64967c6-8d1d-470a-a7c5-63efec2e6499",
  "date_created": "2026-03-02T18:00:57.225000Z",
  "date_modified": "2026-03-02T18:00:57.225000Z",
  "file_hash": "5b90e7e73dc00a43384308357dbfc1b91ff2481a490101b746e9341f92ea90fb",
  "private": false,
  "record": {
    "abstract": "We describe an implicit procedure for solving linear equation systems\nresulting from the discretization of the three dimensional (seven variables)\nlinear Fokker-Planck equation. The discretization of the Fokker-Planck equation\nis performed using a twenty-five point molecule that leads to a coefficient\nmatrix with equal number of diagonals. The method is an extension of Stone\u0027s\nimplicit procedure, includes a vast class of collision terms and can be applied\nto stationary or non stationary problems with different discretizations in\ntime. Test calculations and comparisons with other methods are presented in two\nstationary examples, including an astrophysical application for the\nMiyamoto-Nagai disk potential for a typical galaxy.",
    "arxiv_id": "physics/0505093",
    "authors": [
      "Maximiliano Ujevic",
      "Patricio S. Letelier"
    ],
    "categories": [
      "physics.comp-ph",
      "astro-ph"
    ],
    "doi": "10.1016/j.jcp.2005.11.004",
    "journal_ref": "J.Comput.Phys. 215 (2006) 485-505",
    "title": "Solving procedure for a twenty-five diagonal coefficient matrix: direct   numerical solutions of the three dimensional linear Fokker-Planck equation",
    "url": "https://arxiv.org/abs/physics/0505093"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "e6ba4388-1c09-4297-8294-72d52c2ddb40",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}