Related papers: On the accuracy of symplectic integrators for secu…
The numerical solution of an ordinary differential equation can be interpreted as the exact solution of a nearby modified equation. Investigating the behaviour of numerical solutions by analysing the modified equation is known as backward…
We consider secular perturbations of nearly Keplerian two-body motion under a perturbing potential that can be approximated to sufficient accuracy by expanding it to second order in the coordinates. After averaging over time to obtain the…
Hill's equations are an approximation that is useful in a number of areas of astrophysics including planetary rings and planetesimal disks. We derive a symplectic method for integrating Hill's equations based on a generalized leapfrog. This…
We introduce a class of fourth order symplectic algorithms that are ideal for doing long time integration of gravitational few-body problems. These algorithms have only positive time steps, but require computing the force gradient in…
We present a class of symplectic integrators adapted for the integration of perturbed Hamiltonian systems of the form $H=A+\epsilon B$. We give a constructive proof that for all integer $p$, there exists an integrator with positive steps…
It is well known that numerical errors grow exponentially in $N$-body simulations of gravitational bound stellar systems, but it is not well understood how the accuracy parameters of algorithms affect the physical evolution in simulations.…
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.…
Simulation of many-particle system evolution by molecular dynamics takes to decrease integration step to provide numerical scheme stability on the sufficiently large time interval. It leads to a significant increase of the volume of…
Symplectic integrators with long-term preservation of integrals of motion are introduced for the guiding-center model of plasma particles in toroidal magnetic fields of general topology. An efficient transformation to canonical coordinates…
Symplectic integrators constructed from Hamiltonian and Lie formalisms are obtained as symplectic maps whose flow follows the exact solution of a "sourrounded" Hamiltonian K = H + h^k H_1. Those modified Hamiltonians depends virtually on…
We show that symplectic Runge-Kutta methods provide effective symplectic integrators for Hamiltonian systems with index one constraints. These include the Hamiltonian description of variational problems subject to position and velocity…
The interpretation of defect models heavily relies on software metrics that are used to construct them. However, such software metrics are often correlated to defect models. Prior work often uses feature selection techniques to remove…
In this work, a kernel-based surrogate for integrating Hamiltonian dynamics that is symplectic by construction and tailored to large prediction horizons is proposed. The method learns a scalar potential whose gradient enters a…
We introduce a recent symplectic integration scheme derived for solving physically motivated systems with non-separable Hamiltonians. We show its relevance to Riemannian manifold Hamiltonian Monte Carlo (RMHMC) and provide an alternative to…
Accelerated gradient methods have had significant impact in machine learning -- in particular the theoretical side of machine learning -- due to their ability to achieve oracle lower bounds. But their heuristic construction has hindered…
One of the main endeavors of fundamental astrometry is to establish a practical realization of an inertial reference frame anchored to celestial objects whose positions are defined in the barycentric coordinates of the solar system. The…
We investigate the computational performance of various numerical methods for the integration of the equations of motion and the variational equations for some typical classical many-body models of condensed matter physics: the…
The Simulating eXtreme Spacetimes Collaboration's code SpEC can now routinely simulate binary black hole mergers undergoing $\sim25$ orbits, with the longest simulations undergoing nearly $\sim180$ orbits. While this sounds impressive, the…
Cosmological constraints from clusters rely on accurate gravitational mass estimates, which strongly depend on cluster gas temperature measurements. Therefore, systematic calibration differences may result in biased, instrument-dependent…
In order to perform numerical studies of long-term stability in nonlinear Hamiltonian systems, one needs a numerical integration algorithm which is symplectic. Further, this algorithm should be fast and accurate. In this paper, we propose…