Drift-preserving numerical integrators for stochastic Poisson systems

被引：0

作者：

Cohen, David ^{[1
,2
,3
]}

Vilmart, Gilles ^{[4
]}

机构：

[1] Umea Univ, Dept Math & Math Stat, Umea, Sweden

[2] Chalmers Univ Technol, Dept Math Sci, Gothenburg, Sweden

[3] Univ Gothenburg, Gothenburg, Sweden

[4] Univ Geneva, Sect Math, Geneva, Switzerland

来源：

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS | 2022年 / 99卷 / 01期

基金：

瑞典研究理事会; 瑞士国家科学基金会;

关键词：

Stochastic differential equations; stochastic Hamiltonian systems; stochastic Poisson systems; energy; Casimir; trace formula; numerical schemes; strong convergence; weak convergence; RUNGE-KUTTA METHODS; HAMILTONIAN-SYSTEMS; DIFFERENTIAL-EQUATIONS; WAVE-EQUATIONS; ENERGY; DISCRETIZATION; SIMULATION; INVARIANTS; DRIVEN; STAGE;

D O I：

10.1080/00207160.2021.1922679EN

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We perform a numerical analysis of a class of randomly perturbed Hamiltonian systems and Poisson systems. For the considered additive noise perturbation of such systems, we show the long-time behaviour of the energy and quadratic Casimirs for the exact solution. We then propose and analyse a drift-preserving splitting scheme for such problems with the following properties: exact drift preservation of energy and quadratic Casimirs, mean-square order of convergence 1, weak order of convergence 2. These properties are illustrated with numerical experiments.

引用

页码：4 / 20

页数：17

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