Related papers: Conservative Integrators for Many-body Problems
Numerical integration methods are central to the study of self-gravitating systems, particularly those comprised of many bodies or otherwise beyond the reach of analytical methods. Predictor-corrector schemes, both multi-step methods and…
Many differential equations with physical backgrounds are described as gradient systems, which are evolution equations driven by the gradient of some functionals, and such problems have energy conservation or dissipation properties. For…
We construct Lie point symmetries, a closed-form solution and conservation laws using a non-Noetherian approach for a specific case of the Gorini-Kossakowski-Sudarshan-Lindblad equation that has been recast for the study of non-relativistic…
In this paper we address a class of replicator dynamics, referred as polymatrix replicators, that contains well known classes of evolutionary game dynamics, such as the symmetric and asymmetric (or bimatrix) replicator equations, and some…
Structure-preserving discretization of the Rosenbluth-Fokker-Planck equation is still an open question especially for unlike-particle collision. In this paper, a mass-energy-conserving isotropic Rosenbluth-Fokker-Planck scheme is…
In this paper, we construct high order energy dissipative and conservative local discontinuous Galerkin methods for the Fornberg-Whitham type equations. We give the proofs for the dissipation and conservation for related conservative…
We design an accurate orbital integration scheme for the general N-body problem preserving all the conserved quantities but the angular momentum.This scheme is based on the chain concept (Mikkola & Aarseth 1993) and is regarded as an…
First-order variational equations are widely used in N-body simulations to study how nearby trajectories diverge from one another. These allow for efficient and reliable determinations of chaos indicators such as the Maximal Lyapunov…
This paper concerns the construction and analysis of a numerical scheme for a mixed discrete-continuous fragmentation equation. A finite volume scheme is developed, based on a conservative formulation of a truncated version of the…
It is shown analytically that the energy-conserving implicit nonsymplectic scheme of Bacchini, Ripperda, Chen and Sironi provides a first-order accuracy to numerical solutions of a six-dimensional conservative Hamiltonian system. Because of…
We prove that measure-preserving symmetries of an $n$-dimensional differential system preserve its divergence and the divergence derivatives along the solutions. Also, we prove that measure-preserving reversibilities preserve odd-order…
We reproduce the two-body gravitational conservative dynamics at third post-Newtonian order for spin-less sources by using the effective field theory methods for the gravitationally bound two-body system, proposed by Goldberger and…
We present a class of non-standard numerical schemes which are modifications of the discrete gradient method. They preserve the energy integral exactly (up to the round-off error). The considered class contains locally exact discrete…
In this paper we consider a conservative discretization of the two-dimensional incompressible Navier--Stokes equations. We propose an extension of Arakawa's classical finite difference scheme for fluid flow in the vorticity-stream function…
This work focuses on the development of a self adjusting multirate strategy based on an implicit time discretization for the numerical solution of hyperbolic equations, that could benefit from different time steps in different areas of the…
A numerical dynamical low-rank approximation (DLRA) scheme for the solution of the Vlasov-Poisson equation is presented. Based on the formulation of the DLRA equations as Friedrichs' systems in a continuous setting, it combines recently…
This paper reports a detailed description of the equivalent linear two-body method for the many body problem, which is based on an approximate reduction of the many-body Schroedinger equation by the use of a variational principle. To test…
In the second part of this series, we use the Lagrange multiplier approach proposed in the first part \cite{CheS21} to construct efficient and accurate bound and/or mass preserving schemes for a class of semi-linear and quasi-linear…
Partial differential equations (PDEs) describing thermodynamically isolated systems typically possess conserved quantities (like mass, momentum, and energy) and dissipated quantities (like entropy). Preserving these conservation and…
Conservation properties of iterative methods applied to implicit finite volume discretizations of nonlinear conservation laws are analyzed. It is shown that any consistent multistep or Runge-Kutta method is globally conservative. Further,…