Numerical solution of one-dimensional dispersion equation in homogeneous porous medium by modified finite element method

This article discusses the mathematical modeling of the longitudinal dispersion phenomenon in a homogeneous porous medium and its solution using the modified finite element method. Also, the theorem about existence and uniqueness, and stability of nonlinear system that arose in the numerical scheme, by utilizing nonlinear functional analysis and the Banach fixed point theorem are proved. Finally, illustrations are added to show the efficacy of the derived method.