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A fitted operator method of line scheme for solving two-parameter singularly perturbed parabolic convection-diffusion problems with time delay | ||
| Journal of Mathematical Modeling | ||
| مقاله 11، دوره 11، شماره 2، مهر 2023، صفحه 395-410 اصل مقاله (696.57 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22124/jmm.2023.23001.2039 | ||
| نویسنده | ||
| Naol Tufa Negero* | ||
| Department of Mathematics, Wollega University, Nekemte, Ethiopia | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| Singular perturbation؛ time-delayed parabolic convection-diffusion problems؛ two small parameters؛ the method of line؛ finite difference scheme؛ uniform convergence | ||
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آمار تعداد مشاهده مقاله: 393 تعداد دریافت فایل اصل مقاله: 593 |
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