@Article{NMTMA-8-496,
author = {Devendra Kumar},
title = { Fitted Mesh Method for a Class of Singularly Perturbed Differential-Difference Equations},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2015},
volume = {8},
number = {4},
pages = {496--514},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.2015.my14005},
url = {http://global-sci.org/intro/article_detail/nmtma/12420.html}
}