{
"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"
}
}
}