  We give a possible splitting method to a Hamiltonian for the description of
charged particles moving around the Reissner-Nordstrom-(anti)-de Sitter black
hole with an external magnetic field. This Hamiltonian can be separated into
six analytical solvable pieces, whose solutions are explicit functions of
proper time. In this case, second- and fourth-order explicit symplectic
integrators are easily available. They exhibit excellent long-term behavior in
maintaining the boundness of Hamiltonian errors regardless of ordered or
chaotic orbits if appropriate step-sizes are chosen. Under some circumstances,
an increase of positive cosmological constant gives rise to strengthening the
extent of chaos from the global phase space; namely, chaos of charged particles
occurs easily for the accelerated expansion of the universe. However, an
increase of the magnitude of negative cosmological constant does not. The
different contributions on chaos are because the cosmological constant acts as
a repulsive force in the Reissner-Nordstrom-de Sitter black hole, but an
attractive force in the Reissner-Nordstrom-anti-de Sitter black hole.
