@article {
author = {Negero, Naol Tufa},
title = {A fitted operator method of line scheme for solving two-parameter singularly perturbed parabolic convection-diffusion problems with time delay},
journal = {Journal of Mathematical Modeling},
volume = {11},
number = {2},
pages = {395-410},
year = {2023},
publisher = {University of Guilan},
issn = {2345-394X},
eissn = {2382-9869},
doi = {10.22124/jmm.2023.23001.2039},
abstract = {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.},
keywords = {Singular perturbation,time-delayed parabolic convection-diffusion problems,two small parameters,the method of line,finite difference scheme,uniform convergence},
url = {https://jmm.guilan.ac.ir/article_6601.html},
eprint = {https://jmm.guilan.ac.ir/article_6601_796659fd522b120398d31fc34a7f5dd8.pdf}
}