Second order parameter uniform convergence of a finite element method for a system of ‘n’ partially singularly perturbed delay differential equations of reaction diffusion type

A boundary value problem for a second-order system of `n' partially singularly perturbed delay differential equations of reaction diffusion type is regarded in this article. This problem's solutions has boundary layers at x=0 and x=2 and inner layers at x=1. To handle the problems, a computational analysis based on a finite element method generally accessible to a piecewise-uniform Shishkin mesh is provided. It is shown that the procedure is almost second order convergent in the energy norm uniformly in the perturbation parameters. The hypothesis is supported by numerical examples.