Abstract In this article, the spectral collocation method based on Legendre polynomials is applied to solve the multi‐dimensional temporal‐order Burgers–Huxley transportation problem. The fractional‐order Burgers–Huxley equation models solute transport in porous media by capturing the combined effects of diffusion, convection, and reaction processes. The primary objective of this study is to obtain a numerical solution and visually demonstrate how the nonlinear terms and fractional‐order derivatives affect the solution profile. To validate the proposed method, the results were compared with the available analytical solutions for a particular case of the problem through a detailed error analysis. Both the norm and norm errors are presented in tabulated form, and the absolute error is presented graphically, which confirms the convergence and effectiveness of the proposed scheme.
Singh et al. (Mon,) studied this question.