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In this paper, an implicit nonsymplectic exact energy-preserving integratoris specifically designed for a ten-dimensional phase-space conservativeHamiltonian system with five degrees of freedom. It is based on a suitablediscretization-averaging of the Hamiltonian gradient, with a second-orderaccuracy to numerical solutions. A one-dimensional disordered discretenonlinear Schr\"{o}dinger equation and a post-Newtonian Hamiltonian system ofspinning compact binaries are taken as our two examples. We demonstratenumerically that the proposed algorithm exhibits good long-term performance inthe preservation of energy, if roundoff errors are neglected. This result isindependent of time steps, initial orbital eccentricities, and regular andchaotic orbital dynamical behavior. In particular, the application ofappropriately large time steps to the new algorithm is helpful in reducingtime-consuming and roundoff errors. This new method, combined with fastLyapunov indicators, is well suited related to chaos in the two exampleproblems. It is found that chaos in the former system is mainly responsible forone of the parameters. In the latter problem, a combination of small initialseparations and high initial eccentricities can easily induce chaos.

Energy-conserving integrator for conservative Hamiltonian systems with ten-dimensional phase space