辛几何
数学
哈密顿系统
辛积分器
可分离空间
应用数学
乘法函数
相空间
积分器
数学分析
辛流形
计算机科学
计算机网络
物理
带宽(计算)
热力学
作者
Grigori N. Milstein,Yu. M. Repin,Michael V. Tretyakov
标识
DOI:10.1137/s0036142901395588
摘要
Stochastic Hamiltonian systems with multiplicative noise, phase flows of which preserve symplectic structure, are considered. To construct symplectic methods for such systems, sufficiently general fully implicit schemes, i.e., schemes with implicitness both in deterministic and stochastic terms, are needed. A new class of fully implicit methods for stochastic systems is proposed. Increments of Wiener processes in these fully implicit schemes are substituted by some truncated random variables. A number of symplectic integrators is constructed. Special attention is paid to systems with separable Hamiltonians. Some results of numerical experiments are presented. They demonstrate superiority of the proposed symplectic methods over very long times in comparison with nonsymplectic ones.
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