  We construct a particle integrator for nonrelativistic particles by means of
the splitting method based on the exact flow of the equation of motion of
particles in the presence of constant electric and magnetic field. This
integrator is volume-preserving similar to the standard Boris integrator and is
suitable for long-term integrations in particle-in-cell simulations. Numerical
tests reveal that it is significantly more accurate than previous
volume-preserving integrators with second-order accuracy. For example, in the
$E \times B$ drift test, this integrator is more accurate than the Boris
integrator and the integrator based on the exact solution of gyro motion by
three and two orders of magnitude, respectively. In addition, we derive
approximate integrators that incur low computational cost and high-precision
integrators displaying fourth- to tenth-order accuracy with the aid of the
composition method. These integrators are also volume-preserving. It is also
demonstrated that the Boris integrator is equivalent to the simplest case of
the approximate integrators derived in this study.
