Numerical Analysis for a System of Partially Singularly Perturbed Convection-Diffusion Delay Differential Equations

Objectives: To find efficient numerical method to solve a system of 𝑛- partially singularly perturbed delay differential equations of convection-diffusion type with large spatial delay. Methods: The integration of a classical finite difference scheme with a piecewise uniform Shishkin mesh enhances the resolution of sharp gradients and boundary layers, providing improved accuracy. Findings: The approach is shown to achieve first-order convergence in the maximum norm, with uniform convergence independent of the perturbation parameters, ensuring robustness across various perturbation values. Novelty: The method addresses both boundary and interior layers effectively, which are complex due to the presence of singular perturbation parameters and large spatial delay. The theoretical results are supported by numerical example, validating the practical effectiveness of the proposed method. Keywords: Singularly perturbed delay differential equation; Boundary layers; Interior layers; Finite difference scheme; Maximum norm; Shishkin mesh; Parameter uniform convergence