An Energy-conserving Integrator for Conservative Hamiltonian Systems with Ten-dimensional Phase Space

Abstract In this paper, an implicit nonsymplectic exact energy-preserving integrator is specifically designed for a ten-dimensional phase-space conservative Hamiltonian system with five degrees of freedom. It based on suitable discretization-averaging the gradient, second-order accuracy to numerical solutions. A one-dimensional disordered discrete nonlinear Schrödinger equation and post-Newtonian spinning compact binaries are taken as our two examples. We demonstrate numerically that proposed algorithm exhibits good long-term performance in preservation energy, if roundoff errors neglected. This result independent time steps, initial orbital eccentricities, regular chaotic dynamical behavior. particular, application appropriately large steps new helpful reducing time-consuming errors. method, combined fast Lyapunov indicators, well suited studying influence some parameters or conditions related chaos example problems. found former mainly responsible one parameters. latter problem, combination small separations high eccentricities can easily induce chaos.