scholarly journals Stochastic symplectic Runge–Kutta methods for the strong approximation of Hamiltonian systems with additive noise

2017 ◽  
Vol 325 ◽  
pp. 134-148 ◽  
Author(s):  
Weien Zhou ◽  
Jingjing Zhang ◽  
Jialin Hong ◽  
Songhe Song
Keyword(s):  
Hamiltonian Systems ◽  
Strong Approximation ◽  
Additive Noise ◽  
Runge Kutta

Construction of Symplectic Runge-Kutta Methods for Stochastic Hamiltonian Systems

2016 ◽  
Vol 21 (1) ◽  
pp. 237-270 ◽  
Author(s):  
Peng Wang ◽  
Jialin Hong ◽  
Dongsheng Xu
Keyword(s):  
Case Studies ◽  
Hamiltonian Systems ◽  
Multiplicative Noise ◽  
Additive Noise ◽  
Symplectic Methods ◽  
Computational Tools ◽  
Stochastic Hamiltonian Systems ◽  
Runge Kutta ◽  
Strong Order

AbstractWe 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 Runge-Kutta 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.

scholarly journals Symplectic Integration of Hamiltonian Systems with Additive Noise

2002 ◽  
Vol 39 (6) ◽  
pp. 2066-2088 ◽  
Author(s):  
G. N. Milstein ◽  
Yu. M. Repin ◽  
M. V. Tretyakov
Keyword(s):  
Hamiltonian Systems ◽  
Additive Noise ◽  
Symplectic Integration
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