A hybrid numerical scheme for singular perturbation delay problems with integral boundary condition

In this article, a singular perturbation delay problem of convection–diffusion (C–D) type having an integral boundary condition is considered. The analytical solution of the considered problem has a weak interior layer in addition to the boundary layer at the right end of the domain. Some a priori estimates are given on the exact solution which are useful for the error analysis. The numerical approximation is composed of a hybrid finite difference scheme on a generalized Shishkin mesh. For the proposed scheme, almost second order ε\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varepsilon $$\end{document}-uniform convergence is established. Numerical experiments are conducted to corroborate the theoretical results. A comparison with the existing scheme (J Appl Math Comput 63:813–828) is also performed.