Simulation of orbit RKA3 from Table 1 with the RK4 method (red line, top left), IMR scheme (blue line, top right), Hamiltonian (green line, bottom left), and modified Hamiltonian (magenta line, bottom right) schemes. The central Kerr black hole, rotating from west to east, is shown as a colored sphere of radius r₊. The plots clearly show that the RK4 method introduces numerical errors resulting in a damping of the particle gyration. The other schemes, instead, preserve this feature until the end of the run.