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.markbroyard.com/hot-sale-us-topo-7-5-minute-map-for-sunken-lake-mi-supply-limited-grab/