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A second order numerical method for two-parameter singularly perturbed time-delay parabolic problems | ||
| Journal of Mathematical Modeling | ||
| مقاله 10، دوره 11، شماره 4، اسفند 2023، صفحه 745-766 اصل مقاله (9.91 M) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22124/jmm.2023.24353.2182 | ||
| نویسندگان | ||
| Mekashaw Ali Mohye1؛ Justin B Munyakazi* 2؛ Tekle Gemechu Dinka1 | ||
| 1Department of Applied Mathematics, Adama Science and Technology University, Ethiopia | ||
| 2Department of Mathematics and Applied Mathematics, University of the Western Cape, South Africa | ||
| چکیده | ||
| In this article, a time delay parabolic convection-reaction-diffusion singularly perturbed problem with two small parameters is considered. We investigate the layer behavior of the solution for both smooth and non-smooth data. A numerical method to solve the problems described is developed using the Crank-Nicolson scheme to discretize the time-variable on a uniform mesh while a hybrid finite difference is applied for the space-variable. The hybrid scheme is a combination of the central, upwind and mid-point differencing on a piecewise uniform mesh of Shishkin type. The convergence analysis shows that the proposed method is uniformly convergent of second order in both space and time. Numerical experiments conducted on some test examples confirm the theoretical results. | ||
| کلیدواژه‌ها | ||
| Singular perturbation؛ delay differential equation؛ Shishkin mesh؛ hybrid scheme؛ boundary layers؛ fitted mesh finite difference method؛ uniform convergence | ||
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