{
  "id": "1801.06455",
  "version": "v1",
  "published": "2018-01-19T15:22:23.000Z",
  "updated": "2018-01-19T15:22:23.000Z",
  "title": "Analysis of Some Splitting Schemes for the Stochastic Allen-Cahn Equation",
  "authors": [
    "Charles-Edouard Bréhier",
    "Ludovic Goudenège"
  ],
  "categories": [
    "math.NA",
    "math.AP",
    "math.PR"
  ],
  "abstract": "We introduce and analyze an explicit time discretization scheme for the one-dimensional stochastic Allen-Cahn, driven by space-time white noise. The scheme is based on a splitting strategy, and uses the exact solution for the nonlinear term contribution. We first prove boundedness of moments of the numerical solution. We then prove strong convergence results: first, L^2 ($\\Omega$)-convergence of order almost 1/4, localized on an event of arbitrarily large probability, then convergence in probability of order almost 1/4. The theoretical analysis is supported by numerical experiments, concerning strong and weak orders of convergence.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-19T15:22:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stochastic allen-cahn equation",
      "splitting schemes",
      "explicit time discretization scheme",
      "one-dimensional stochastic allen-cahn",
      "strong convergence results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}