Advancing numerical solutions for a system of singularly perturbed delay differential equations at linear rate

This work introduces a numerical technique designed to efficiently solve a specific type of differential equations known as a weakly coupled system of singularly perturbed delay differential equations. The innovation of this approach stems from its unique integration of three key elements: the Numerov method, known for its accuracy in solving second-order ODEs; a fitting factor, which improves handling of the singular perturbation parameter essential for accurately modeling SPDDEs; and the Taylor series expansion, which approximates first-order derivative terms, facilitating the application of the Numerov method to the system. Numerical experiments are conducted with varying perturbation parameters and mesh sizes to validate the method’s effectiveness. The results, expressed in terms of maximum absolute errors and the rate of convergence, demonstrate that the proposed approach achieves first-order uniform convergence.