Energy corrections in Hamiltonian dynamics simulations

Abstract

We study two energy-correction algorithms for numerical simulations of Hamiltonian systems. The first algorithm, which corrects a trajectory after-the-fact, can significantly improve symplectic integrators by achieving a higher order of energy accuracy. The second algorithm, which corrects a trajectory along-the-way, can drastically improve the conventional Runge-Kutta schemes both in energy conservation and trajectory accuracy. We present extended numerical simulation results for a nonlinear oscillator and the well-known Hénon-Heiles model that exhibits chaotic dynamics.