Related papers: High order symplectic integrators for perturbed Ha…
A novel symplectic integrator for Hamiltonian equations on $S_2^n \times T^{\ast} \RR^m$ is developed and studied. Partitioned Runge--Kutta methods for Hamiltonian systems on products of Hamiltionian manifolds are studied, specifically,…
The adaptive perturbation method decomposes a Hamiltonian by the diagonal elements and non-diagonal elements of the Fock state. The diagonal elements of the Fock state are solvable but can contain the information about coupling constants.…
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…
This paper investigates a class of non-autonomous highly oscillatory ordinary differential equations characterized by a linear component inversely proportional to a small parameter $\varepsilon$, with purely imaginary eigenvalues, and an…
In this article we introduce a low order implicit symplectic integrator designed to follow the Hamiltonian flow as close as possible. This integrator is obtained by the method of Liouvillian forms and does not require particular hypotheses…
We give a possible splitting method to a Hamiltonian for the description of charged particles moving around the Reissner-Nordstrom-(anti)-de Sitter black hole with an external magnetic field. This Hamiltonian can be separated into six…
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 because not all variables can be separable, or not all…
Variational integrators are derived for structure-preserving simulation of stochastic Hamiltonian systems with a certain type of multiplicative noise arising in geometric mechanics. The derivation is based on a stochastic discrete…
Nonadiabatic behavior of metastable systems modeled by anharmonic Hamiltonians is reproduced by the Fokker-Planck and imaginary time Schrodinger equation scheme with subsequent symplectic integration. Example solutions capture ergodicity…
We present a simple algorithm to switch between $N$-body time integrators in a reversible way. We apply it to planetary systems undergoing arbitrarily close encounters and highly eccentric orbits, but the potential applications are broader.…
In this paper, we consider a class of highly oscillatory Hamiltonian systems which involve a scaling parameter $\varepsilon\in(0,1]$. The problem arises from many physical models in some limit parameter regime or from some time-compressed…
We introduce a new family of symplectic integrators depending on a real parameter. When the paramer is zero, the corresponding method in the family becomes the classical Gauss collocation formula of order 2s, where s denotes the number of…
Symplectic integrators are widely implemented numerical integrators for Hamiltonian mechanics, which preserve the Hamiltonian structure (symplecticity) of the system. Although the symplectic integrator does not conserve the energy of the…
Multi-derivative one-step methods based upon Euler-Maclaurin integration formulae are considered for the solution of canonical Hamiltonian dynamical systems. Despite the negative result that simplecticity may not be attained by any…
Symplectic integrators are the tool of choice for many researchers studying dynamical systems because of their good long-term energy conservation properties. For systems with a dominant central mass, symplectic integrators are also highly…
Symplectic integrators offer many advantages for the numerical solution of Hamiltonian differential equations, including bounded energy error and the preservation of invariant sets. Two of the central Hamiltonian systems encountered in…
In this work we develop some fifth-order integrable coupled systems of weight $0$ and $1$ which possess seventh-order symmetry. We establish four new systems, where in some cases, related recursion operator and bi-Hamiltonian formulations…
Recently, our group developed explicit symplectic methods for curved spacetimes that are not split into several explicitly integrable parts, but are via appropriate time transformations. Such time-transformed explicit symplectic integrators…
This paper is a survey on exponential integrators to solve cubic-quintic complex Ginzburg-Landau equations and related stiff problems. In particular, we are interested in accurate computation near the pulsating and exploding soliton…
Hamiltonian systems of ordinary and partial differential equations are fundamental mathematical models spanning virtually all physical scales. A critical property for the robustness and stability of computational methods in such systems is…