Advanced Fitted Mesh Finite Difference Strategies for Solving ‘n’ Two-Parameter Singularly Perturbed Convection–Diffusion System

This paper proposes a robust finite difference method on a fitted Shishkin mesh to solve a system of n singularly perturbed convection–reaction–diffusion differential equations with two small parameters. Defined on the interval [0,1], this system exhibits boundary layers due to the presence of small parameters, making accurate numerical approximations challenging. The method employs a piecewise uniform Shishkin mesh that adapts to layer regions and efficiently captures the solution’s behavior. The scheme is proven to be uniformly convergent with respect to the perturbation parameters, achieving nearly first-order accuracy. Comprehensive numerical experiments validate the theoretical results, illustrating the method’s robustness and efficiency in handling parameter-sensitive boundary layers.