Stochastic symplectic methods based on the Padé approximations for linear stochastic Hamiltonian systems

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• 作者：Liying Sun ; Lijin Wang ; ^{ljwang@ucas.ac.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Padé ; approximation ; Linear stochastic Hamiltonian systems ; Symplectic methods ; Root-mean-square convergence order
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：311
• 期：Complete
• 页码：439-456
• 全文大小：725 K

文摘

In this article, we propose a kind of numerical methods based on the Padé approximations, for two kinds of stochastic Hamiltonian systems. For the general linear stochastic Hamiltonian systems, it is shown that the applied Padé approximations dba" title="Click to view the MathML source">P_(k,k)$P_{(k,k)}$ produce numerical solutions that are symplectic, and the proposed numerical schemes based on P_(r,s)$P_{(r,s)}$ are of root-mean-square convergence order $\frac{r+s}{2}$. For a special kind of linear stochastic Hamiltonian systems with additive noises, the numerical methods using two kinds of Padé approximations, $P_{(\hat{r},\hat{s})}$ and $P_{(\check{r},1)}$, possess root-mean-square convergence order $\check{r}+2$ when $\hat{r}+\hat{s}=\check{r}+3$, and are symplectic if $\hat{r}=\hat{s}$. These generalize the Padé approximation approaches for symplectic integration of linear Hamiltonian systems to the stochastic context.