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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.

65L10Boundary value problems for ODE (numerical methods)
34K10Boundary value problems for functional-differential equations
65L12Finite difference methods for ODE (numerical methods)
65L50Mesh generation and refinement (ODE)
34K28Numerical approximation of solutions of functional-differential equations
34K26Singular perturbations of functional-differential equations
Full Text: DOI
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