Numerical solution of nonlinear reaction advection-diffusion equation using the modified collocation method

Abstract

This article presents a numerical solution of the nonlinear reaction-advection-diffusion equation with specified initial and boundary conditions using a modified cubic B-spline collocation method. Nonlinear terms are linearised using the Crank-Nicholson method. The derived numerical scheme is shown to be unconditionally convergent through stability analysis. The accuracy of the numerical scheme has been verified by its application to the three standard instances. The numerical findings are then compared with the existing analytical results by employing the l2 and l∞ error norms. The main feature of this article is the graphical presentation of the numerical solution of the concerned model for different sets of advection, diffusion and reaction coefficients to show the effect on the solute profile when advection and diffusion terms are both nonlinear. Nonlinear reaction-advection-diffusion equations have found applications in diverse areas like groundwater and water pollution studies. © 2025 E-M. Craciun et al., published by Sciendo.