University of GuilanJournal of Mathematical Modeling2345-394X11220230701A fitted operator method of line scheme for solving two-parameter singularly perturbed parabolic convection-diffusion problems with time delay395410660110.22124/jmm.2023.23001.2039ENNaol TufaNegeroDepartment of Mathematics, Wollega University, Nekemte, Ethiopia0000-0003-1593-735XJournal Article20220928This paper presents a parameter-uniform numerical scheme for the solution of two-parameter singularly perturbed parabolic convection-diffusion problems with a delay in time. The continuous problem is semi-discretized using the Crank-Nicolson finite difference method in the temporal direction. The resulting differential equation is then discretized on a uniform mesh using the fitted operator finite difference method of line scheme. The method is shown to be accurate in $ O(\left(\Delta t \right)^{2} + N^{-2}) $, where $ N $ is the number of mesh points in spatial discretization and $ \Delta t $ is the mesh length in temporal discretization. The parameter-uniform convergence of the method is shown by establishing the theoretical error bounds. Finally, the numerical results of the test problems validate the theoretical error bounds.https://jmm.guilan.ac.ir/article_6601_796659fd522b120398d31fc34a7f5dd8.pdf