{
  "id": "2207.10484",
  "version": "v1",
  "published": "2022-07-21T13:59:51.000Z",
  "updated": "2022-07-21T13:59:51.000Z",
  "title": "Splitting schemes for FitzHugh--Nagumo stochastic partial differential equations",
  "authors": [
    "Charles-Edouard Bréhier",
    "David Cohen",
    "Giuseppe Giordano"
  ],
  "categories": [
    "math.NA",
    "cs.NA",
    "math.PR"
  ],
  "abstract": "We design and study splitting integrators for the temporal discretization of the stochastic FitzHugh--Nagumo system. This system is a model for signal propagation in nerve cells where the voltage variable is solution of a one-dimensional parabolic PDE with a cubic nonlinearity driven by additive space-time white noise. We first show that the numerical solutions have finite moments. We then prove that the splitting schemes have, at least, the strong rate of convergence $1/4$. Finally, numerical experiments illustrating the performance of the splitting schemes are provided.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-07-21T13:59:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fitzhugh-nagumo stochastic partial differential equations",
      "splitting schemes",
      "additive space-time white noise",
      "cubic nonlinearity driven",
      "stochastic fitzhugh-nagumo system"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}