{
  "id": "2202.01683",
  "version": "v1",
  "published": "2022-02-03T16:49:49.000Z",
  "updated": "2022-02-03T16:49:49.000Z",
  "title": "On the properties of the exceptional set for the randomized Euler and Runge-Kutta schemes",
  "authors": [
    "Tomasz Bochacik"
  ],
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "We show that the probability of the exceptional set decays exponentially for a broad class of randomized algorithms approximating solutions of ODEs, admitting a certain error decomposition. This class includes randomized explicit and implicit Euler schemes, and the randomized two-stage Runge-Kutta scheme (under inexact information). We design a confidence interval for the exact solution of an IVP and perform numerical experiments to illustrate the theoretical results.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-02-03T16:49:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "randomized euler",
      "properties",
      "implicit euler schemes",
      "randomized two-stage runge-kutta scheme",
      "exceptional set decays"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}