High-order stochastic symplectic partitioned Runge-Kutta methods for stochastic Hamiltonian systems with additive noise
作者：
Highlights：
• A simple class of stochastic partitioned Runge-Kutta methods (SPRKs) is proposed.
• Global mean-square order conditions and symplectic conditions are discussed.
• 2-stage Diagonal-implicit symplectic methods of order 1.5 are presented.
• Explicit 1.5-order symplectic methods for separable systems are developed.
• Get some explicit 2.0-order symplectic methods for second-order separable systems.
摘要
•A simple class of stochastic partitioned Runge-Kutta methods (SPRKs) is proposed.•Global mean-square order conditions and symplectic conditions are discussed.•2-stage Diagonal-implicit symplectic methods of order 1.5 are presented.•Explicit 1.5-order symplectic methods for separable systems are developed.•Get some explicit 2.0-order symplectic methods for second-order separable systems.
论文关键词：Stochastic Hamiltonian system,Stochastic partitioned Runge–Kutta method,Symplectic integrator
论文评审过程：Received 1 May 2018, Revised 9 October 2018, Accepted 15 October 2018, Available online 7 November 2018, Version of Record 7 November 2018.
论文官网地址：https://doi.org/10.1016/j.amc.2018.10.041
