12 citations · 32 across the 12 of their papers we have counts for
12 papers
A novel class of high-order uniformly accurate exponential integrators with local linear extension for the charged-particle dynamics under strong magnetic field
Lina Wang, Bin Wang, Beibei Zhu
In this paper, we develop a novel class of high-order uniformly accurate exponential integrators for charged-particle dynamics under a strong magnetic field. The small parameter $0…
Implementation and (Inverse Modified) Error Analysis for implicitly-templated ODE-nets
Aiqing Zhu, Tom Bertalan, Beibei Zhu +2
We focus on learning unknown dynamics from data using ODE-nets templated on implicit numerical initial value problem solvers. First, we perform Inverse Modified error analysis of t…
Explicit K-symplectic methods for nonseparable non-canonical Hamiltonian systems
Beibei Zhu, Lun Ji, Aiqing Zhu +1
We propose efficient numerical methods for nonseparable non-canonical Hamiltonian systems which are explicit, K-symplectic in the extended phase space with long time energy conserv…
On Numerical Integration in Neural Ordinary Differential Equations
Aiqing Zhu, Pengzhan Jin, Beibei Zhu +1
The combination of ordinary differential equations and neural networks, i.e., neural ordinary differential equations (Neural ODE), has been widely studied from various angles. Howe…
Poisson Integrators based on splitting method for Poisson systems
Beibei Zhu, Lun Ji, Aiqing Zhu +1
We propose Poisson integrators for the numerical integration of separable Poisson systems. We analyze three situations in which the Poisson systems are separated in three ways and…
VPNets: Volume-preserving neural networks for learning source-free dynamics
Aiqing Zhu, Beibei Zhu, Jiawei Zhang +2
We propose volume-preserving networks (VPNets) for learning unknown source-free dynamical systems using trajectory data. We propose three modules and combine them to obtain two net…
Spectrally accurate space-time solution of Manakov systems
Luigi Barletti, Luigi Brugnano, Yifa Tang +1
In this paper, we study the numerical solution of Manakov systems by using a spectrally accurate Fourier decomposition in space, coupled with a spectrally accurate time integration…
Word-series high-order averaging of highly oscillatory differential equations with delay
J. M. Sanz-Serna, Beibei Zhu
We show that, for appropriate combinations of the values of the delay and the forcing frequency, it is possible to obtain easily high-order averaged versions of periodically forced…
High-order stroboscopic averaging methods for highly oscillatory delay problems
M. P. Calvo, J. M. Sanz-Serna, Beibei Zhu
We introduce and analyze a family of heterogeneous multiscale methods for the numerical integration of highly oscillatory systems of delay differential equations with constant dela…
Bogdanov-Takens resonance in time-delayed systems
Mattia Coccolo, BeiBei Zhu, Miguel A. F. Sanjuán +1
We analyze the oscillatory dynamics of a time-delayed dynamical system subjected to a periodic external forcing. We show that, for certain values of the delay, the response can be…
A stroboscopic averaging algorithm for highly oscillatory delay problems
J. M. Sanz-Serna, Beibei Zhu
We propose and analyze a heterogenous multiscale method for the efficient integration of constant-delay differential equations subject to fast periodic forcing. The stroboscopic av…
Symplectic methods for non-canonical Hamiltonian systems
Beibei Zhu, Ruili Zhang, Yifa Tang +1
We show that, when applied to any non-canonical Hamiltonian system, any integrator that is symplectic for canonical Hamiltonian problems is actually conjugate symplectic for the no…