%0 Journal Article
%T A fitted operator method of line scheme for solving two-parameter singularly perturbed parabolic convection-diffusion problems with time delay
%J Journal of Mathematical Modeling
%I University of Guilan
%Z 2345-394X
%A Negero, Naol Tufa
%D 2023
%\ 07/01/2023
%V 11
%N 2
%P 395-410
%! A fitted operator method of line scheme for solving two-parameter singularly perturbed parabolic convection-diffusion problems with time delay
%K Singular perturbation
%K time-delayed parabolic convection-diffusion problems
%K two small parameters
%K the method of line
%K finite difference scheme
%K uniform convergence
%R 10.22124/jmm.2023.23001.2039
%X This 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.
%U https://jmm.guilan.ac.ir/article_6601_796659fd522b120398d31fc34a7f5dd8.pdf