TY - JOUR T1 - Fitted Mesh Method for a Class of Singularly Perturbed Differential-Difference Equations AU - Devendra Kumar JO - Numerical Mathematics: Theory, Methods and Applications VL - 4 SP - 496 EP - 514 PY - 2015 DA - 2015/08 SN - 8 DO - http://doi.org/10.4208/nmtma.2015.my14005 UR - https://global-sci.org/intro/article_detail/nmtma/12420.html KW - AB -

This paper deals with a more general class of singularly perturbed boundary value problem for a differential-difference equations with small shifts. In particular, the numerical study for the problems where second order derivative is multiplied by a small parameter $ε$ and the shifts depend on the small parameter $ε$ has been considered. The fitted-mesh technique is employed to generate a piecewise-uniform mesh, condensed in the neighborhood of the boundary layer. The cubic B-spline basis functions with fitted-mesh are considered in the procedure which yield a tridiagonal system which can be solved efficiently by using any well-known algorithm. The stability and parameter-uniform convergence analysis of the proposed method have been discussed. The method has been shown to have almost second-order parameter-uniform convergence. The effect of small parameters on the boundary layer has also been discussed. To demonstrate the performance of the proposed scheme, several numerical experiments have been carried out.