An Ε-Uniform Method for Singularly Perturbed 2D Convection Dominated Elliptic Boundary Value Problems with Delay and Advance

This article investigates linear two-dimensional elliptic singularly perturbed problems with delay and advance terms in both directions of the reaction terms, showcasing regular boundary layer behavior in its solution. In this area, prior research has been limited to one-dimensional problems. We approximate the delay and advance terms using Taylor series expansion and develop a numerical method based on finite difference approaches. Rigorous analysis is conducted to prove parameter uniform a priori estimates. Numerical experiments are implemented to reveal the effect of the delay and advance terms on the solution. Overall, this study provides new insights into the behavior of these types of problems and presents a robust numerical method for their solution.