Conservative Integrators for Many-body Problems

Abstract

Conservative symmetric second-order one-step schemes are derived for dynamical systems describing various many-body systems using the Discrete Multiplier Method. This includes conservative schemes for the $n$-species Lotka-Volterra system, the $n$-body problem with radially symmetric potential and the $n$-point vortex models in the plane and on the sphere. In particular, we recover Greenspan-Labudde's conservative schemes for the $n$-body problem. Numerical experiments are shown verifying the conservative property of the schemes and second-order accuracy.

arXiv comment35 pages

References in corpus (4)

• A novel formulation of point vortex dynamics on the sphere: geometrical and numerical aspects
• The multiplier method to construct conservative finite difference schemes for ordinary and partial differential equations
• Conservative methods for dynamical systems
• On the arbitrarily long-term stability of conservative methods

Cited by in corpus (4)

• On the design of energy-decaying momentum-conserving integrator for nonlinear dynamics using energy splitting and perturbation techniques
• Conservative Integrators for Vortex Blob Methods
• Minimal ${\ell }^2$ Norm Discrete Multiplier Method
• Improving sampling efficacy on high dimensional distributions with thin high density regions using Conservative Hamiltonian Monte Carlo