Published online by Cambridge University Press: 10 November 2015
This paper deals with a more general class of singularly perturbed boundary valueproblem for a differential-difference equations with small shifts. Inparticular, the numerical study for the problems where second order derivativeis multiplied by a small parameter ε and the shifts depend on thesmall parameter ε has been considered. The fitted-mesh technique isemployed to generate a piecewise-uniform mesh, condensed in the neighborhood ofthe boundary layer. The cubic B-spline basis functions with fitted-mesh areconsidered in the procedure which yield a tridiagonal system which can besolved efficiently by using any well-known algorithm. The stability andparameter-uniform convergence analysis of the proposed method have beendiscussed. The method has been shown to have almost second-orderparameter-uniform convergence. The effect of small parameters on the boundarylayer has also been discussed. To demonstrate the performance of the proposedscheme, several numerical experiments have been carried out.