[en] A numerical model is described that may be used to investigate important effects of dust charging on ion waves and instabilities in dusty plasmas. The model considers a three species system with fluid electrons and ions and particle-in-cell PIC charged dust grains in which the dust charge on the grains varies in time according to the standard charging model. Waves in magnetized or unmagnetized dusty plasmas can be considered. Fundamental effects of dust charging on wave modes which include the dust charge fluctuation mode and damping of ion waves are considered. Also important effects of dust charging on waves produced by the expansion of dust into a background plasma are discussed. Finally an ion acoustic instability that is due to dust charging is investigated. These examples show that there is good agreement with past theoretical predictions on dust charge fluctuation effects and also numerical simulations provide useful additional insight into the physical processes involved. (orig.)