 Stochastic symplectic partitioned Runge–Kutta methods for stochastic Hamiltonian systems with multiplicative noiseQiang Ma and Xiaohua Ding Applied Mathematics and Computation, 2015, vol. 252, issue C, 520-534 Abstract: Some new stochastic partitioned Runge–Kutta (SPRK) methods are proposed for the strong approximation of partitioned stochastic differential equations (SDEs). The order conditions up to strong global order 1.0 are calculated. The SPRK methods are applied to solve stochastic Hamiltonian systems with multiplicative noise. Some conditions are captured to guarantee that a given SPRK method is symplectic. It is shown that stochastic symplectic partitioned Runge–Kutta (SSPRK) methods can be written in terms of stochastic generating functions. In addition, this paper also proves that the SSPRK methods can conserve the quadratic invariants of original stochastic systems. Based on the order and symplectic conditions, some low-stage SSPRK methods with strong global order 1.0 are constructed. Finally, some numerical results are presented to demonstrate the efficiency of the SSPRK methods. Keywords: Stochastic Hamiltonian systems; Stochastic differential equations; Symplectic integrators; Stochastic generating functions; Stochastic partitioned Runge–Kutta methods (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:252:y:2015:i:c:p:520-534 DOI: 10.1016/j.amc.2014.12.045 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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