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

作者：

Highlights：

• Symplectic schemes of high strong order for Hamiltonian systems with additive noise.

• Totally derivative-free Runge–Kutta schemes are proposed.

• Mean-square order 2.0 schemes for a class of second-order Hamiltonian systems.

• Linear growth property can be exactly preserved for linear oscillator.

摘要

•Symplectic schemes of high strong order for Hamiltonian systems with additive noise.•Totally derivative-free Runge–Kutta schemes are proposed.•Mean-square order 2.0 schemes for a class of second-order Hamiltonian systems.•Linear growth property can be exactly preserved for linear oscillator.

论文关键词：Stochastic differential equations,Stochastic Runge–Kutta methods,Symplectic integrators,Mean-square convergence

论文评审过程：Received 22 May 2016, Revised 27 April 2017, Available online 10 May 2017, Version of Record 20 May 2017.

论文官网地址：https://doi.org/10.1016/j.cam.2017.04.050