A Paul trap or quadrupole ion trap is a device designed to confine ions or charged particles in a given space. It consists of four electrodes that produce electric fields varying in time. The voltage applied to these electrodes varies harmonically with low frequency (quasi-static regime), which simplifies the model. The goal of this project is to numerically simulate in matlab a Paul trap and the motion of the ions trapped in it by discretizing the Poisson equation and applying the method of moments (MoM), first in 2D and then generalized to 3D 2019/2020