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Hybrid method for numerical solution of singularly perturbed delay differential equations. (English) Zbl 1120.65088
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.
##### MSC:
 65L10 Boundary value problems for ODE (numerical methods) 34K10 Boundary value problems for functional-differential equations 65L12 Finite difference methods for ODE (numerical methods) 65L50 Mesh generation and refinement (ODE) 34K28 Numerical approximation of solutions of functional-differential equations 34K26 Singular perturbations of functional-differential equations