Specifics of numerical simulations of the trajectories of charged particles in pulsed electric fields

The problem of numerical simulation of the trajectories of charged particles as applied to the pulsed electric fields, is considered. Typical numerical recipes imply that the right hand side function of the differential equations is smooth and can be differentiated up to necessary order; however, when applied to the functions with sharp jumps these recipes can result to serious inaccuracies of the calculations. The paper considers the true inaccuracy artifacts which exists for the pulsed functions (pulsed electric fields) when some "smooth" numerical recipes are used for trajectory integration. It also considers some simple modifications of the standard tracing algorithms which enable to eliminate these artifact effects.