TY - JOUR
T1 - Construction of Symplectic Runge-Kutta Methods for Stochastic Hamiltonian Systems
AU - Peng Wang, Jialin Hong & Dongsheng Xu
JO - Communications in Computational Physics
VL - 1
SP - 237
EP - 270
PY - 2018
DA - 2018/04
SN - 21
DO - http://doi.org/10.4208/cicp.261014.230616a
UR - https://global-sci.org/intro/article_detail/cicp/11239.html
KW - 
AB - <p style="text-align: justify;">We study the construction of symplectic Runge-Kutta methods for stochastic
Hamiltonian systems (SHS). Three types of systems, SHS with multiplicative noise,
special separable Hamiltonians and multiple additive noise, respectively, are considered
in this paper. Stochastic Runge-Kutta (SRK) methods for these systems are investigated,
and the corresponding conditions for SRK methods to preserve the symplectic
property are given. Based on the weak/strong order and symplectic conditions, some
effective schemes are derived. In particular, using the algebraic computation, we obtained
two classes of high weak order symplectic Runge-Kutta methods for SHS with
a single multiplicative noise, and two classes of high strong order symplectic RungeKutta
methods for SHS with multiple multiplicative and additive noise, respectively.
The numerical case studies confirm that the symplectic methods are efficient computational
tools for long-term simulations.</p>