Second-Order Robust Numerical Method for a Partially Singularly Perturbed Time-Dependent Reaction–Diffusion System

This article aims at the development and analysis of a numerical scheme for solving singularly perturbed parabolic system n reaction–diffusion equations where m (with m<n) contain perturbation parameter while rest do not it. The is based on uniform mesh in temporal variable piecewise Shishkin spatial variable, together with classical finite difference approximations. Some analytical properties error analyses are derived. Furthermore, bound provided. Under certain assumptions, it proved that proposed has almost second-order convergence space direction first-order time variable. Errors increase when ε→0, proving convergence. experiments presented, which support theoretical results.