Hybrid method for numerical solution of singularly perturbed delay differential equations (Q883882)

This paper deals with the numerical technique for singularly perturbed second-order differential-difference equations of the convection-diffusion type with a small delay parameter \(\delta\) whose solution has a single boundary layer. The authors analyze three difference operators \(L_k^N, k=1,2,3\) with a simple upwind scheme, a midpoint upwind scheme and a hybrid scheme, respectively, on a Shishkin mesh to approximate the solution of the problem. The hybrid algorithm uses central difference in the boundary layer region and a midpoint upwind scheme outside the boundary layer. The autors establish that the hybrid scheme gives better accuracy. The paper concludes with a few numerical results exhibiting the performance of these three schemes.