26 citations · 28 across the 8 of their papers we have counts for
8 papers
Symmetric-adjoint and symplectic-adjoint methods and their applications
Geng Sun, Siqing Gan, Hongyu Liu +1
Symmetric method and symplectic method are classical notions in the theory of Runge-Kutta methods. They can generate numerical flows that respectively preserve the symmetry and sym…
Numerical invariant tori of symplectic integrators for integrable Hamiltonian systems
Zhaodong Ding, Zaijiu Shang
In this paper, we study the persistence of invariant tori of integrable Hamiltonian systems satisfying Rüssmann's non-degeneracy condition when symplectic integrators are applied t…
Exponential Stability Estimate of Symplectic Integrators for Integrable Hamiltonian Systems
Zhaodong Ding, Zaijiu Shang, Bo Xie
We prove a Nekhoroshev-type theorem for nearly integrable symplectic map. As an application of the theorem, we obtain the exponential stability symplectic algorithms. Meanwhile, we…
A KAM-Theorem for Persistence of Quasi-periodic Invariant Tori in Bifurcation Theory of Equilibrium Points
Xuemei Li, Zaijiu Shang
In this paper, we establish a KAM-theorem for ordinary differential equations with finitely differentiable vector fields and multiple degeneracies. The theorem can be used to deal…
Quasi-periodic solutions for differential equations with an elliptic-type degenerate equilibrium point under small perturbations
Xuemei Li, Zaijiu Shang
This work focuses on the existence of quasi-periodic solutions for ordinary and delay differential equations (ODEs and DDEs for short) with an elliptic-type degenerate equilibrium…
Two Single-shot Methods for Locating Multiple Electromagnetic Scatterers
Jingzhi Li, Hongyu Liu, Zaijiu Shang +1
We develop two inverse scattering schemes for locating multiple electromagnetic (EM) scatterers by the electric far-field measurement corresponding to a single incident/detecting p…
Singular perturbation of reduced wave equation and scattering from an embedded obstacle
Hongyu Liu, Zaijiu Shang, Hongpeng Sun +1
We consider time-harmonic wave scattering from an inhomogeneous isotropic medium supported in a bounded domain (). {In a subregion , the…
Preservation of stability properties near fixed points of linear hamiltonian systems by symplectic integrators
Xiaohua Ding, Hongyu Liu, Zaijiu Shang +2
Based on reasonable testing model problems, we study the preservation by symplectic Runge-Kutta method (SRK) and symplectic partitioned Runge-Kutta method (SPRK) of structures for…