Numerical method for solving weakly coupled systems of singularly perturbed delay differential equations

This article introduces an effective numerical method for solving a weakly coupled system of singularly perturbed delay differential equations. The approach involves approximating the first-order derivative in the system using a Taylor series, followed by the application of finite difference technique. A scheme that incorporates a fitting factor is developed for problem resolution. To assess the accuracy of the method, error estimation is conducted using the maximum principle, and theoretical justifications are supported by relevant numerical examples involving varying perturbation parameters and mesh sizes. The numerical results are presented in terms of maximum absolute errors and the rate of convergence. Our approach is demonstrated to be first order uniformly convergent, as evident from the tabulated values. In comparison to previously published methodologies, the present approach offers improved results and contributes to the existing literature.