Efficient Layer-Resolving Fitted Mesh Finite Difference Approach for Solving a System of n Two-Parameter Singularly Perturbed Convection–Diffusion Delay Differential Equations

This paper presents a robust fitted mesh finite difference method for solving a system of n singularly perturbed two parameter convection–reaction–diffusion delay differential equations defined on the interval [0,2]. Leveraging a piecewise uniform Shishkin mesh, the method adeptly captures the solution’s behavior arising from delay term and small perturbation parameters. The proposed numerical scheme is rigorously analyzed and proven to be parameter-robust, exhibiting nearly first-order convergence. A numerical illustration is included to validate the method’s efficiency and to confirm the theoretical predictions.