Improved Reproducing Kernel Method for Singularly Perturbed Differential-Difference Equations with Boundary Layer Behavior

This paper is devoted to the numerical treatment of singularly perturbed differential-difference equations with small delay whose solutions exhibiting boundary layer. The reproducing kernel method presented in the previous work is not valid for singularly perturbed differential-difference equations with small delay. In this work, we will improve the reproducing kernel method in order to obtain accurate approximation to the solutions of considered singularly perturbed differential-difference equations. Two numerical examples are provided to show the performance of the present scheme.