Study and analysis of nonlinear (2+1)-dimensional solute transport equation in porous media

Abstract

In the present endeavour, the shifted Legendre collocation method is extended to obtain the solution of nonlinear fractional order (2+1)-dimensional advection–reaction–diffusion solute transport equation. The variations of solute concentration of the model for different fractional order space and time derivatives are presented graphically for various particular cases. The main feature of the present contribution is the graphical exhibitions of the effects of advection term, reaction term and fractional-order parameters on the solution profile. To authenticate the effectiveness of the method, a drive has been taken to compare the obtained results with the existing analytical results of the integer-order form of the considered model through error analysis which are displayed in tabular and pictorial forms. © 2021 International Association for Mathematics and Computers in Simulation (IMACS)