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A numerical method based on the moving mesh for the solving of a mathematical model of the avascular tumor growth | ||
| Computational Methods for Differential Equations | ||
| مقاله 1، دوره 9، شماره 2، تیر 2021، صفحه 327-346 اصل مقاله (589.65 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2020.31455.1472 | ||
| نویسندگان | ||
| Mina Bagherpoorfard1؛ Ali Reza Soheili* 2 | ||
| 1Department of applied mathematics, Ferdowsi university of Mashhad, Mashhad. Iran. | ||
| 2Department of applied mathematics, Ferdowsi university of Mashhad, Mashhad, Iran. | ||
| چکیده | ||
| Using adaptive mesh methods is one of the strategies to improve numerical solutions in time dependent partial differential equations. The moving mesh method is an adaptive mesh method, which, firstly does not need an increase in the number of mesh points, secondly reduces the concentration of points in the steady areas of the solutions that do not need a high degree of accuracy, and finally places the points in the areas, where a high degree of accuracy is needed. In this paper, we improved the numerical solutions for a three-phase model of avascular tumor growth by using the moving mesh method. The physical formulation of this model uses reaction-diffusion dynamics with the mass conservation law and appears in the format of the nonlinear system of partial differential equations based on the continuous density of three proliferating, quiescent, and necrotic cell categorizations. Our numerical results show more accurate numerical solutions, as compared to the corresponding fixed mesh method. Moreover, this method leads to the higher order of numerical convergence. | ||
| کلیدواژهها | ||
| Adaptive moving mesh؛ Tumor growth؛ Avascular tumor growth؛ Mathematical modeling | ||
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آمار تعداد مشاهده مقاله: 593 تعداد دریافت فایل اصل مقاله: 517 |
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