We have developed an efficient computational scheme for integration of the classical Hamilton equations describing the ion dynamics confined in the radio-frequency field of the Paul trap. It has permitted a quantitative treatment of cold atom-ion resonant collisions in hybrid atom-ion traps with taking into account unremovable ion micromotion caused by the radio-frequency fields (V. S. https://www.roneverhart.com/Roland-Blues-Cube-Stage-1x12-60-Watt-Combo-Amp-p24291/