26 citations · 28 across the 8 of their papers we have counts for
4 papers · 1 filter
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…