  In this work, we consider the error estimates of some splitting schemes for
the charged-particle dynamics under a strong magnetic field. We first propose a
novel energy-preserving splitting scheme with computational cost per step
independent from the strength of the magnetic field. Then under the maximal
ordering scaling case, we establish for the scheme and in fact for a class of
Lie-Trotter type splitting schemes, a uniform (in the strength of the magnetic
field) and optimal error bound in the position and in the velocity parallel to
the magnetic field. For the general strong magnetic field case, the modulated
Fourier expansions of the exact and the numerical solutions are constructed to
obtain a convergence result. Numerical experiments are presented to illustrate
the error and energy behaviour of the splitting schemes.
