Symplectic integrators that preserve the geometric structure of Hamiltonian flows and do not
exhibit secular growth in energy errors are suitable for the long-term integration of N-body …

In previous papers, explicit symplectic integrators were designed for nonrotating black holes,
such as a Schwarzschild black hole. However, they fail to work in the Kerr spacetime …

We give a possible splitting method to a Hamiltonian for the description of charged particles
moving around the Reissner–Nordström-(anti)-de Sitter black hole with an external magnetic …

This paper deals mainly with the application of the second-order symplectic implicit midpoint
rule and its symmetric compositions to a post-Newtonian Hamiltonian formulation with …

We refine the recently developed fourth-order extended phase space explicit symplectic-like
methods for inseparable Hamiltonians using Yoshida's triple product combined with a …

For the approximate solution of the Kepler equations and some related problems, a fourth-
order convergent functionally-fitted block hybrid Falkner method which is based on the …

Численное моделирование является мощным средством для исследования орбит
небесных тел. Оно стало уже почти традиционным в современной практике. Значение …

We modify the logarithmic Hamiltonian of Mikkola and Tanikawa by adding a constant (or
function) to both the kinetic energy and the force function. Explicit symplectic algorithms are …

We develop a brand-new method of manifold correction that extends Nacozy's approach to
correcting individual Kepler energies that vary with time in n-body problems of planetary …

For each object of an n-body problem in planetary dynamics, orbital elements except the
mean anomaly are directly determined by five independently slow-varying quantities or …