arXiv subjects

Qingyi Zhan

Publications and source records attributed to Qingyi Zhan.

4 recordsLinked to original sources

arXiv2024

Numerical integrations of stochastic contact Hamiltonian systems via stochastic contact Hamilton-Jacobi equation

Stochastic contact Hamiltonian systems are a class of important mathematical models, which can describe the dissipative properties with odd dimensions in the stochastic environment. In this article, we investigate the numerical dynamics of the stochastic contact Hamiltonian systems via structure-preserving methods. The contact structure-preserving schemes are constructed by the stochastic contact Hamilton-Jacobi equation. A general numerical approximation method of the stochastic contact Hamilton-Jacobi equation is devised, and the convergent order theorem is provided, too. Numerical tests are shown to confirm the theoretical results and the usability of proposed approach.

math.NA↗

arXiv2022

Numerical integration of stochastic contact Hamiltonian systems via stochastic Herglotz variational principle

In this work we construct a stochastic contact variational integrator and its discrete version via stochastic Herglotz variational principle for stochastic contact Hamiltonian systems. A general structure-preserving stochastic contact method is devised, and the stochastic contact variational integrators are established. The implementation of this approach is validated by the numerical experiments.

math.NA↗

arXiv2020

Symplectic method for Hamiltonian stochastic differential equations with multiplicative Lévy noise in the sense of Marcus

A class of Hamiltonian stochastic differential equations with multiplicative Lévy noise in the sense of Marcus, and the construction and numerical implementation methods of symplectic Euler scheme, are considered. A general symplectic Euler scheme for this kind of Hamiltonian stochastic differential equations is devised, and its convergence theorem is proved. The second part presents realizable numerical implementation methods for this scheme in details. Some numerical experiments are conducted to demonstrate the effectiveness and superiority of the proposed method by the simulations of its orbits, Hamlitonian,and convergence order over a long time interval.

math.NA↗

arXiv2020

Symplectic Euler scheme for Hamiltonian stochastic differential equations driven by Levy noise

This paper proposes a general symplectic Euler scheme for a class of Hamiltonian stochastic differential equations driven by L$\acute{e}$vy noise in the sense of Marcus form. The convergence of the symplectic Euler scheme for this Hamiltonian stochastic differential equations is investigated. Realizable numerical implementation of this scheme is also provided in details. Numerical experiments are presented to illustrate the effectiveness and superiority of the proposed method by the simulations of its orbits, symplectic structure and Hamlitonian.

math.NA↗