Evolution of the relative error in the initial radius for orbit B (left panel) and D (right panel) simulated with Δt = 1 (solid lines), Δt = 0.1 (dashed lines), and Δt = 0.01 (dashed–dotted lines) until t = 500. The Hamiltonian scheme (green lines) performs better than the RK4 (red lines), IMR (blue lines), and modified Hamiltonian (magenta lines) schemes, triggering the linear growth of error and the release of the particle from the (physically unstable) bound orbits at much later times.