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Fitted mesh numerical scheme for singularly perturbed delay reaction diffusion problem with integral boundary condition | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 19 بهمن 1401 اصل مقاله (2.3 MB) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2023.49239.2054 | ||
| نویسندگان | ||
Getu Mekonnen Wondimu1؛ Tekle Gemechu Dinka1؛ Mesfin Woldaregay   1؛ Gemechis File Duressa 2
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| 1Department of Applied Mathematics, Adama Science and Technology University, Adama, Ethiopia. | ||
| 2Department of Mathematics, Jimma University, Jimma, Ethiopia. | ||
| چکیده | ||
| This article presents a numerical treatment of the singularly perturbed delay reaction diffusion problem with an integral boundary condition. In the considered problem, a small parameter ", is multiplied on the higher order derivative term. The presence of this parameter causes the existence of boundary layers in the solution. The solution also exhibits an interior layer because of the large spatial delay. Simpson’s 1/3 rule is applied to approximate the integral boundary condition given on the right end of the domain. A standard finite difference scheme on piecewise uniform Shishkin mesh is proposed to discretize the problem in the spatial direction, and the Crank-Nicolson method is used in the temporal direction. The developed numerical scheme is parameter uniformly convergent, with orders of convergence almost two in space and two in time. Two numerical examples are considered to validate the theoretical results. | ||
| کلیدواژه‌ها | ||
| Singularly perturbed problems؛ Fitted Mesh scheme؛ Integral boundary condition | ||
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آمار تعداد مشاهده مقاله: 35 تعداد دریافت فایل اصل مقاله: 94 |
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