Parameter uniform numerical method for a system of singularly perturbed parabolic convection–diffusion equations.

This article presents a numerical study of the initial boundary value problem for a singularly perturbed system of two equations of convection–diffusion type. The perturbation parameter in both equations leads to the boundary layer in both solution components. The sign of the convection coefficient decides the position of the boundary layer at the right end of the spatial domain. We suggest a numerical method composed of a spline-based scheme with a Shishkin mesh for solving the proposed system. Convergence analysis shows that the numerical technique is nearly second-order uniformly convergent concerning the perturbation parameter. The numerical illustration is delivered to support the theoretical results. • The systems of singularly perturbed problems are challenging to solve numerically. • To effectively resolve the boundary layers, this paper offers a novel concept. • The cubic spline basis functions are used to solve problems with wild behavior. • The boundary layer is resolved using Shishkin mesh. • The convergence of the numerical approach is proved theoretically. [ABSTRACT FROM AUTHOR]