Since the first detection of gravitational waves by the LIGO/VIRGO team, the
related research field has attracted more attention. The spinning compact
binaries system, as one of the gravitational-wave sources for broadband laser
interferometers, has been widely studied by related researchers. In order to
analyze the gravitational wave signals using matched filtering techniques,
reliable numerical algorithms are needed. Spinning compact binaries systems in
Post-Newtonian (PN) celestial mechanics have an inseparable Hamiltonian. The
extended phase-space algorithm is an effective solution for the problem of this
system. We have developed correction maps for the extended phase-space method
in our previous work, which significantly improves the accuracy and stability
of the method with only a momentum scale factor. In this paper, we will add
more scale factors to modify the numerical solution in order to minimize the
errors in the constants of motion. However, we find that these correction maps
will result in a large energy bias in the subterms of the Hamiltonian in
chaotic orbits, whose potential and kinetic energy, etc. are calculated
inaccurately. We develop new correction maps to reduce the energy bias of the
subterms of the Hamiltonian, which can instead improve the accuracy of the
numerical solution and also provides a new idea for the application of the
manifold correction in other algorithms.
