Open AccessNumerical methods preserving multiple Hamiltonians for stochastic Poisson systems
Author(s) -
Lijin Wang,
Pengjun Wang,
Yanzhao Cao
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series s
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.481
H-Index - 34
eISSN - 1937-1632
pISSN - 1937-1179
DOI - 10.3934/dcdss.2021095
Subject(s) - poisson distribution , invariant (physics) , mathematics , projection (relational algebra) , casimir effect , convergence (economics) , algorithm , physics , mathematical physics , quantum mechanics , statistics , economics , economic growth
In this paper, we propose a class of numerical schemes for stochastic Poisson systems with multiple invariant Hamiltonians. The method is based on the average vector field discrete gradient and an orthogonal projection technique. The proposed schemes preserve all the invariant Hamiltonians of the stochastic Poisson systems simultaneously, with possibility of achieving high convergence orders in the meantime. We also prove that our numerical schemes preserve the Casimir functions of the systems under certain conditions. Numerical experiments verify the theoretical results and illustrate the effectiveness of our schemes.