Computational method based on reproducing kernel for solving singularly perturbed differential-difference equations with a delay

摘要

In this paper, Reproducing Kernel Hilbert Space Method (RKHSM) based on collocation scheme is used to solve singularly perturbed second order differential-difference equations. We implement RKHSM without Gram–Schmidt orthogonalization process for singularly perturbed differential-difference equation with boundary layer behavior and also oscillatory behavior with small delay. RKHSM in this study, is based on the division of the problem domain into two subintervals, one with boundary layer and the other one without such a boundary layer. Several numerical examples are studied to demonstrate the accuracy of the present method. Results of the present scheme indicate that new algorithm has the following advantages: small computational work, fast convergence, and high precision.