ANALYSIS OF SOLUTE TRANSPORT IN FINITE SOIL COLUMNS USING FRACTIONAL-ORDER MODEL AND SPECTRAL COLLOCATION METHOD

In this study, we introduce a spectral collocation approach to solve a fractional-order nonlinear reaction–convection–diffusion equation, which is a prototypical model for solute transport. This model explores the transportation of solutes in a finite soil column length through interactions among diffusion transport, convection effects, and reaction mechanisms. A shifted Legendre polynomial is employed in the technique to approximate the multidimensional nonlinear reaction–convection–diffusion in a fractional-order system. The use of shifted Legendre polynomials provides an effective compromise between computational simplicity, accuracy, and stability, making them a robust choice for the present fractional order nonlinear reaction–convection–diffusion model. The primary objective of this study is to determine the solution and demonstrate graphically how the nonlinear reaction term, convection term, and fractional-order derivatives affect the solution profile for the considered model. To validate the proposed method, we compared it with existing analytical solutions for a specific case of the problem and performed an error analysis for confirmation. The results, including the absolute error and [Formula: see text]-norm error, are presented in pictorial and tabular forms.