4 papers
A unified framework of energy-stable splitting exponential integrators for damped Hamiltonian systems
Lu Li, Xiaoli Li, Zaijiu Shang +1
In this work, we study long-time numerical integration of Hamiltonian systems subject to linear perturbations. We assume the energy-compatible linear-damping condition, which ensur…
A class of generalized Nesterov's accelerated gradient method from dynamical perspective
Xu Cheng, Jiaqi Liu, Zaijiu Shang
We propose a class of \textit{Euler-Lagrange} equations indexed by a pair of parameters () that generalizes Nesterov's accelerated gradient methods for convex () and stro…
The elliptical invariant tori of nearly integrable Hamiltonian system through symplectic algorithms
Zaijiu Shang, Yang Xu
In this paper we apply symplectic algorithms to nearly integrable Hamiltonian system, and prove it can maintain lots of elliptic lower dimensional invariant tori. We are committed…
A KAM theorem of symplectic algorithms for nearly integrabel Hamiltonian systems
Zaijiu Shang, Yang Xu
In this paper we prove a KAM-like theorem of symplectic algorithms for nearly integrable Hamiltonian systems which generalises the result of \cite{r1} and \cite{r6} for the case of…