The numerical solution of the singularly perturbed differential-difference equations based on the Meshless method

Abstract

In this paper, we describe a meshless approach to solve singularly perturbed differential-difference equations of the second order with boundary layer at one end of the interval. In the numerical treatment for such type of problems, first we approximate the terms containing negative and positive shifts which converts it to a singularly perturbed differential equation. Next, a numerical scheme based on the moving least squares (MLS) method is used for solving singularly perturbed differential equation. The MLS methodology is a meshless method, because it does not need any background mesh or cell structures. The proposed scheme is simple and efficient to approximate the unknown function. Several examples are presented to demonstrate the efficiency and validity of the numerical scheme presented in the paper.