Singularly Perturbed Convection-Diffusion Turning Point Problem with Shifts

In this paper, a class of singularly perturbed turning point problem with shifts (i.e., delay as well as advance) is considered. Presence of turning point results into twin boundary layers in the solution of the problem under consideration. For the numerical approximation of the problem, a finite difference scheme is proposed on a uniform mesh. Interpolation is used to tackle the terms containing shifts and to deal with the difficulty arising due to presence of the turning point a combination of backward and forward difference is used in the first derivative term. Convergence analysis is given for the proposed numerical scheme. Numerical results are presented which illustrate the theoretical results and depict the effect of shifts on the layer behavior of the solution.