Fitted mesh B-spline collocation method for singularly perturbed differential–difference equations with small delay

Abstract

This paper deals with the singularly perturbed boundary value problem for a linear second order differential–difference equation of the convection–diffusion type with small delay parameter of whose solution has a boundary layer. The fitted mesh technique is employed to generate a piecewise-uniform mesh, condensed in the neighborhood of the boundary layers. B-spline collocation method is used with fitted mesh. Parameter-uniform convergence analysis of the method is discussed. The method is shown to have almost second order parameter-uniform convergence. The effect of small delay on boundary layer has also been discussed. Several examples are considered to demonstrate the performance of the proposed scheme and how the size of the delay argument and the coefficient of the delay term affects the layer behavior of the solution.