University of Guilan Journal of Mathematical Modeling 2345-394X 11 4 2023 12 01 A second order numerical method for two-parameter singularly perturbed time-delay parabolic problems 745 766 7121 10.22124/jmm.2023.24353.2182 EN Mekashaw Ali Mohye Department of Applied Mathematics, Adama Science and Technology University, Ethiopia Justin B Munyakazi Department of Mathematics and Applied Mathematics, University of the Western Cape, South Africa Tekle Gemechu Dinka Department of Applied Mathematics, Adama Science and Technology University, Ethiopia Journal Article 2023 04 20 In this article, a time delay parabolic convection-reaction-diffusion singularly perturbed  problem with two small parameters is considered. We investigate the layer behavior of the  solution for both smooth and non-smooth data. A numerical method to solve the problems described is developed using the Crank-Nicolson scheme to discretize the time-variable on a  uniform mesh while a hybrid finite difference is applied for the space-variable. The hybrid  scheme is a combination of the central, upwind and mid-point differencing on a piecewise uniform mesh of Shishkin type. The convergence analysis shows that the proposed method is  uniformly convergent of second order in both  space and   time. Numerical experiments  conducted on some test examples confirm the theoretical results. https://jmm.guilan.ac.ir/article_7121_a79358436e5a87849221d87c57a5e845.pdf