an incremental-analytical solution for variable-coefficient advection-diffusion equations in simulating river flow

The advection-diffusion equation (ade) is used for modeling physical phenomena. however, solving these equations with dominating advection term is often come across difficulties most of which are the numerical dispersion and oscillation. methodologies used to solve these equations are rather complex numerical procedures with tedious computational works. in this work, a new incremental-analytical solution is proposed to solve ade; with gaussian impulse and step function as input. less computational difficulties and numerical dispersions are the results of implementing the proposed method. also, as compared to series of standards presented in the literatures, this method proved its accuracy and thus can be used to simulate actual rivers with less computational errors.