{
  "id": "1812.09036",
  "version": "v1",
  "published": "2018-12-21T10:26:25.000Z",
  "updated": "2018-12-21T10:26:25.000Z",
  "title": "Adaptive time-stepping for Stochastic Partial Differential Equations with non-Lipschitz drift",
  "authors": [
    "Stuart Campbell",
    "Gabriel Lord"
  ],
  "comment": "25 pages, 4 figures",
  "categories": [
    "math.NA"
  ],
  "abstract": "We introduce an explicit, adaptive time-stepping scheme for simulation of SPDEs with non-Lipschitz drift coefficients. Strong convergence is proven for the full space-time discretisation with multiplicative noise by considering the space and time discretisation separately. Adapting the time-step size to ensure strong convergence is shown numerically to produce more accurate solutions when compared to alternative fixed time-stepping strategies for the same computational effort.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-21T10:26:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65C30",
      "60H15"
    ],
    "keywords": [
      "stochastic partial differential equations",
      "adaptive time-stepping",
      "full space-time discretisation",
      "non-lipschitz drift coefficients",
      "ensure strong convergence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}