  We present a detailed comparison of several integration schemes applied to
the dynamic system consisting of a charged particle on the Kerr background
endowed with the axisymmetric electromagnetic test field. In particular, we
compare the performance of the symplectic integrator with several
non-symplectic routines and discuss under which circumstances we should choose
the symplectic one and when we should switch to some other scheme. We are
basically concerned with two crucial, yet opposing aspects - accuracy of the
integration and CPU time consumption. The latter is generally less critical in
our application while the highest possible accuracy is strongly demanded.
