  In recent publications, the construction of explicit symplectic integrators
for Schwarzschild and Kerr type spacetimes is based on splitting and
composition methods for numerical integrations of Hamiltonians or
time-transformed Hamiltonians associated with these spacetimes. Such splittings
are not unique but have various choices. A Hamiltonian describing the motion of
charged particles around the Schwarzschild black hole with an external magnetic
field can be separated into three, four and five explicitly integrable parts.
It is shown through numerical tests of regular and chaotic orbits that the
three-part splitting method is the best one of the three Hamiltonian splitting
methods in accuracy. In the three-part splitting, optimized fourth-order
partitioned Runge-Kutta and Runge-Kutta-Nystr\"{o}m explicit symplectic
integrators exhibit the best accuracies. In fact, they are several orders of
magnitude better than the fourth-order Yoshida algorithms for appropriate time
steps. The former algorithms need small additional computational cost compared
with the latter ones. Optimized sixth-order partitioned Runge-Kutta and
Runge-Kutta-Nystr\"{o}m explicit symplectic integrators have no dramatic
advantages over the optimized fourth-order ones in accuracies during long-term
integrations due to roundoff errors. The idea finding the integrators with the
best performance is also suitable for Hamiltonians or time-transformed
Hamiltonians of other curved spacetimes including the Kerr type spacetimes.
When the numbers of explicitly integrable splitting sub-Hamiltonians are as
small as possible, such splitting Hamiltonian methods would bring better
accuracies. In this case, the optimized fourth-order partitioned Runge-Kutta
and Runge-Kutta-Nystr\"{o}m methods are worth recommending.
