{
  "id": "1411.7572",
  "version": "v1",
  "published": "2014-11-27T12:35:37.000Z",
  "updated": "2014-11-27T12:35:37.000Z",
  "title": "A posteriori error estimates for leap-frog and cosine methods for second order evolution problems",
  "authors": [
    "Emmanuil H. Georgoulis",
    "Omar Lakkis",
    "Charalambos Makridakis",
    "Juha M. Virtanen"
  ],
  "comment": "16 pages, 10 figures, submitted to journal",
  "categories": [
    "math.NA"
  ],
  "abstract": "We consider second order explicit and implicit two-step time-discrete schemes for wave-type equations. We derive optimal order aposteriori estimates controlling the time discretization error. Our analysis, has been motivated by the need to provide aposteriori estimates for the popular leap-frog method (also known as Verlet's method in molecular dynamics literature); it is extended, however, to general cosine-type second order methods. The estimators are based on a novel reconstruction of the time-dependent component of the approximation. Numerical experiments confirm similarity of convergence rates of the proposed estimators and of the theoretical convergence rate of the true error.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-27T12:35:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65M15",
      "65M60",
      "65M06"
    ],
    "keywords": [
      "second order evolution problems",
      "posteriori error estimates",
      "cosine methods",
      "optimal order aposteriori estimates",
      "cosine-type second order methods"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1411.7572G"
    }
  }
}