DEFECT CORRECTION METHOD FOR THE SOLUTION OF SINGULARLY PERTURBED CONVECTION- DIFFUSION PROBLEMS

Abstract

Singularly perturbed convection–diffusion problems exhibit boundary layers that cause spuri ous oscillations for standard finite difference schemes on uniform meshes. We design a high erorder parameter-uniform finite difference method using a defect correction approach that cou ples a stable low-order scheme with a higher-order correction on layer-adapted Shishkin-type meshes, including Bakhvalov–Shishkin and polynomial-Shishkin variants. Rigorous analysis and numerical experiments confirm the method’s robustness and superior convergence behav ior compared to classical upwind and existing collocation-based methods.