{
  "id": "1512.04194",
  "version": "v1",
  "published": "2015-12-14T06:51:40.000Z",
  "updated": "2015-12-14T06:51:40.000Z",
  "title": "Symplectic methods based on Pad$\\acute{e}$ approximation for some stochastic Hamiltonian systems",
  "authors": [
    "Liying Sun",
    "Lijin Wang"
  ],
  "categories": [
    "math.NA"
  ],
  "abstract": "In this article, we introduce a kind of numerical schemes, based on Pad$\\acute{e}$ approximation, for two stochastic Hamiltonian systems which are treated separately. For the linear stochastic Hamiltonian systems, it is shown that the applied Pad$\\acute e$ approximations $P_{(k,k)}$ give numerical solutions that inherit the symplecticity and the proposed numerical schemes based on $P_{(r,s)}$ are of mean-square order $\\frac{r+s}{2}$ under appropriate conditions. In case of the special stochastic Hamiltonian systems with additive noises, the numerical method using two kinds of Pad$\\acute e$ approximation $P_{(\\hat r,\\hat s)}$ and $P_{(\\check r,\\check s)}$ has mean-square order $\\check r+\\check s+1$ when $\\hat r+\\hat s=\\check r+\\check s+2$. Moreover, the numerical solution is symplectic if $\\hat r=\\hat s$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-14T06:51:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "symplectic methods",
      "approximation",
      "mean-square order",
      "special stochastic hamiltonian systems",
      "linear stochastic hamiltonian systems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}