Gaussian Quadrature for Two-Point Singularly Perturbed Boundary Value Problems with Exponential Fitting

Abstract

In this paper, the Gaussian quadrature method with exponential fitting is proposed for the solution of two-point singularly perturbed boundary value problems with layer at one endpoint, dual boundary layers and internal boundary layers. The given boundary value problem is reduced into an equivalent first order differential equation with the perturbation parameter as deviating argument. Then, Gaussian two-point quadrature technique with exponential fitting is implemented to solve the first order equation with deviating parameter. The analysis of the convergence of the method is discussed. Several numerical examples are illustrated with a layer at one end, a layer at two ends and internal layers. Comparison of maximum errors in the solution of the examples with other methods is shown to justify the method.