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.
Negero, N. T. (2023). A fitted operator method of line scheme for solving two-parameter singularly perturbed parabolic convection-diffusion problems with time delay. Journal of Mathematical Modeling, 11(2), 395-410. doi: 10.22124/jmm.2023.23001.2039
MLA
Naol Tufa Negero. "A fitted operator method of line scheme for solving two-parameter singularly perturbed parabolic convection-diffusion problems with time delay". Journal of Mathematical Modeling, 11, 2, 2023, 395-410. doi: 10.22124/jmm.2023.23001.2039
HARVARD
Negero, N. T. (2023). 'A fitted operator method of line scheme for solving two-parameter singularly perturbed parabolic convection-diffusion problems with time delay', Journal of Mathematical Modeling, 11(2), pp. 395-410. doi: 10.22124/jmm.2023.23001.2039
VANCOUVER
Negero, N. T. A fitted operator method of line scheme for solving two-parameter singularly perturbed parabolic convection-diffusion problems with time delay. Journal of Mathematical Modeling, 2023; 11(2): 395-410. doi: 10.22124/jmm.2023.23001.2039
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