{
  "annotation_id": "537e085a-7404-4ed1-abd3-33c90ecae922",
  "date_created": "2026-03-02T18:01:25.187000Z",
  "date_modified": "2026-03-02T18:01:25.187000Z",
  "file_hash": "838d038ea3fa10387cf101a167e9b926bc0fede6897198b5067afe86a6694eb1",
  "private": false,
  "record": {
    "abstract": "A new method for numerical solving of boundary problem for ordinary\ndifferential equations with slowly varying coefficients which is aimed at\nbetter representation of solutions in the regions of their rapid oscillations\nor exponential increasing (decreasing) is proposed. It is based on\napproximation of the solution to find in the form of superposition of certain\npolynomial- exponential basic functions. The method is studied for the\nHelmholtz equation in comparison with the standard finite difference method.\nThe numerical tests have shown the convergence of the method proposed. In\ncomparison with the finite difference method the same accuracy is obtained on\nsubstantially rarer mesh. This advantage becomes more pronounced, if the\nsolution varies very rapidly.",
    "arxiv_id": "physics/9908020",
    "authors": [
      "V. E. Moiseenko",
      "V. V. Pilipenko"
    ],
    "categories": [
      "physics.comp-ph",
      "physics.plasm-ph"
    ],
    "title": "Local Solution Method for Numerical Solving of the Wave Propagation   Problem",
    "url": "https://arxiv.org/abs/physics/9908020"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "dd2816d3-1988-4bf9-b093-b73c5ae89b23",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}