Abstract
Motivated by our recent publication in ([9]), which was supported during the academic year 2016/1437 by the Deanship of Scientific Research in Project 1175, we will develop the previous mathematical model into a two-dimensional model of the transition equations of some pollutants and their rapid spread in a particular liquid, taking into account the given stability analysis of the numerical method which based on finite difference time scheme combined with Galerkin special approximation. This method has been given by our published work in ([12]).