Gaussian quadrature method for solving differential difference equations having boundary layers

Abstract

In this paper, the Gaussian quadrature method is described for the solution of differential difference problems having boundary layers. The given problem is replaced by an asymptotically equivalent first order differential equation with the perturbation parameter as deviating argument. Then, Gaussian two point quadrature is implemented to solve this first order differential equation with perturbation parameter as deviating parameter. Several numerical problems are illustrated to demonstrate the layer behaviour. Comparison of maximum errors in the solution of the problems is made with other methods available in the literature to demonstrate the applicability of the present method.