{
  "id": "2005.07978",
  "version": "v1",
  "published": "2020-05-16T13:01:27.000Z",
  "updated": "2020-05-16T13:01:27.000Z",
  "title": "Numerical solution of linear differential equations with discontinuous coefficients and Henstock integral",
  "authors": [
    "Sergey Lukomskii",
    "Dimitry Lukomskii"
  ],
  "comment": "1 figure",
  "categories": [
    "math.CA"
  ],
  "abstract": "In this article we consider the problem of approximative solution of linear differential equations $y'+p(x)y=q(x)$ with discontinuous coefficients $p$ and $q$. We assume that coefficients of such equation are Henstock integrable functions. To find the approximative solution we change the original Cauchy problem to another problem with piecewise-constant coefficients. The sharp solution of this new problems is the approximative solution of the original Cauchy problem. We find the degree approximation in terms of modulus of continuity $\\omega_\\delta (P),\\ \\omega_\\delta (Q)$, where $P$ and $Q$ are $f$-primitive for coefficients $p$ and $q$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-16T13:01:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34B05",
      "G.1.7"
    ],
    "keywords": [
      "linear differential equations",
      "discontinuous coefficients",
      "henstock integral",
      "numerical solution",
      "original cauchy problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}