Symplectic methods based on Pad\acutee approximation for some stochastic Hamiltonian systems

2015/12/14 by Sun, Liying, Wang, Lijin
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1512.04194

Abstract

In this article, we introduce a kind of numerical schemes, based on Pad\acutee 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 (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_{( r, s)} and P_{(\check r,\check s)} has mean-square order \check r+\check s+1 when r+ s=\check r+\check s+2. Moreover, the numerical solution is symplectic if r= s.

Related

• Modified equations for weak stochastic symplectic schemes via their generating functions
• Symplectic methods for stochastic Hamiltonian systems: asymptotic error distributions and Hamiltonian-specific analysis
• Numerical Methods for Stochastic Systems Preserving Symplectic Structure
• Stochastic modified equations for symplectic methods applied to rough Hamiltonian systems based on the Wong--Zakai approximation
• Symplectic method for Hamiltonian stochastic differential equations with multiplicative Lévy noise in the sense of Marcus