Finite Difference Scheme for a Coupled System of Singularly Perturbed Time-Dependent Delay Initial Value Problems with same perturbation parameter

Objectives: This article focuses on the development of finite difference scheme for solving a coupled system of singularly perturbed time-dependent Robin-type initial value problems with delay and same perturbation parameter. Methods: A mesh refinement-based finite difference scheme is constructed on uniform and piecewise uniform Shishkin mesh on the temporal and spatial domains, respectively. In order to get a better analysis of the solution’s layer phenomena, the solution component is further decomposed into regular and layer components. Analytical and stability results are derived. Using bounds of solution components, the resulting error estimate is established. Findings: The proposed scheme proved to have almost first-order convergence. To support the theoretical findings, an example problem is constructed which validates the proposed scheme. Novelty: The present work focuses on the study of a solution’s layer behavior when the perturbation parameter is the same, rather than different, and provides detailed analytical and numerical analysis. Keywords: Coupled system, Singular perturbation problems, Robin initial conditions, Delay, Shishkin mesh