相关论文: Numerical solution of perturbed Kepler problem usi…

We propose a variational splitting technique for the generalized-$\alpha$ method to solve hyperbolic partial differential equations. We use tensor-product meshes to develop the splitting method, which has a computational cost that grows…

Here we provide an overview of what is known, and what is not known, about an interesting dynamical system known as the Kepler-Heisenberg problem. The main idea is to pose a version of the classical Kepler problem of planetary motion, but…

We consider a completely integrable system of differential equations in arbitrary dimensions whose phase space contains an open set foliated by periodic orbits. This research analyzes the persistence and stability of the periodic orbits…

Context. Due to our increasing knowledge on the Galactic and stellar neighborhood of the Solar System, modern long-period comet motion studies have to take into account both stellar perturbations and the overall Galactic potential. Aims.…

A research on a possibility of trapping a particle with permanent electric dipole in an electrostatic field has been conducted. For cylindrical coaxial electrodes, Keplerian orbits for some particles were revealed. The exact criterion of…

We describe a method for determining a complete set of integrals for a classical Hamiltonian that separates in orthogonal subgroup coordinates. As examples, we use it to determine complete sets of integrals, polynomial in the momenta, for…

We provide a comprehensive survey of splitting and composition methods for the numerical integration of ordinary differential equations (ODEs). Splitting methods constitute an appropriate choice when the vector field associated with the ODE…

This paper reviews the standard algorithm for converting spacecraft state vectors to Keplerian orbital elements with a focus on its computer implementation. It analyzes the shortcomings of the scheme as described in the literature, and…

The two-particle models in de Sitter space-time with time-asymmetric retarded-advanced interactions are constructed. Particular cases of the field-type electromagnetic and scalar interactions are considered. The manifestly covariant…

Forward time step integrators are splitting algorithms with only positive splitting coefficients. When used in solving physical evolution equations, these positive coefficients correspond to positive time steps. Forward algorithms are…

The present work provides a comprehensive study of symmetric-conjugate operator splitting methods in the context of linear parabolic problems and demonstrates their additional benefits compared to symmetric splitting methods. Relevant…

While symplectic integration methods based on operator splitting are well established in many branches of science, high order methods for Hamiltonian systems that split in more than two parts have not been studied in great detail. Here, we…

This paper is an attempt to solve an important class of hypersingular integral equations of the second kind. To this end, we apply a new weighted and modified perturbation method which includes some special cases of the Adomian…

The goal of the paper is to develop a method that will combine the use of variational techniques with regularization methods in order to study existence and multiplicity results for the periodic and the Dirichlet problem associated to the…

Operator splitting methods tailored to coupled linear port-Hamiltonian systems are developed. We present algorithms that are able to exploit scalar coupling, as well as multirate potential of these coupled systems. The obtained algorithms…

Geometric integrators of the Schr\"{o}dinger equation conserve exactly many invariants of the exact solution. Among these integrators, the split-operator algorithm is explicit and easy to implement, but, unfortunately, is restricted to…

We study the interaction of a two-level atom and two fields, one of them classical. We obtain an effective Hamiltonian for this system by using a method recently introduced that produces a small rotation to the Hamiltonian that allows to…

We present a hierarchical computation approach for solving finite-time optimal control problems using operator splitting methods. The first split is performed over the time index and leads to as many subproblems as the length of the…

In this work we present a new methodology for orbit propagation, the hybrid perturbation theory, based on the combination of an integration method and a prediction technique. The former, which can be a numerical, analytical or…

In this paper we study the performance of a symplectic numerical integrator based on the splitting method. This method is applied to a subtle problem i.e. higher order resonance of the elastic pendulum. In order to numerically study the…