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We give a possible splitting method to a Hamiltonian for the description ofcharged particles moving around the Reissner-Nordstrom-(anti)-de Sitter blackhole with an external magnetic field. This Hamiltonian can be separated intosix analytical solvable pieces, whose solutions are explicit functions ofproper time. In this case, second- and fourth-order explicit symplecticintegrators are easily available. They exhibit excellent long-term behavior inmaintaining the boundness of Hamiltonian errors regardless of ordered orchaotic orbits if appropriate step-sizes are chosen. Under some circumstances,an increase of positive cosmological constant gives rise to strengthening theextent of chaos from the global phase space; namely, chaos of charged particlesoccurs easily for the accelerated expansion of the universe. However, anincrease of the magnitude of negative cosmological constant does not. Thedifferent contributions on chaos are because the cosmological constant acts asa repulsive force in the Reissner-Nordstrom-de Sitter black hole, but anattractive force in the Reissner-Nordstrom-anti-de Sitter black hole.

Construction of explicit symplectic integrators in general relativity. III. Reissner-Nordstrom-(anti)-de Sitter black holes