An orthogonal spline collocation method for singularly perturbed parabolic reaction–diffusion problems with time delay

In this article, a numerical technique is developed and analyzed for singularly perturbed delay parabolic reaction–diffusion problems with Dirichlet boundary condition. An orthogonal spline collocation method with C1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C^1$$\end{document}-cubic spline basis functions on a Shishkin mesh is used in the spatial direction. In the temporal direction Crank–Nicolson method on an equidistant mesh is used. An extensive analysis has been undertaken to establish the uniform convergence with respect to the perturbation parameter. To support the theoretical findings, numerical experiments have been presented.