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Wondimu, Getu Mekonnen, Dinka, Tekle Gemechu, Woldaregay, Mesfin, Duressa, Gemechis File. (1402). Fitted mesh numerical scheme for singularly perturbed delay reaction diffusion problem with integral boundary condition. سامانه مدیریت نشریات علمی, 11(3), 478-494. doi: 10.22034/cmde.2023.49239.2054
Getu Mekonnen Wondimu; Tekle Gemechu Dinka; Mesfin Woldaregay; Gemechis File Duressa. "Fitted mesh numerical scheme for singularly perturbed delay reaction diffusion problem with integral boundary condition". سامانه مدیریت نشریات علمی, 11, 3, 1402, 478-494. doi: 10.22034/cmde.2023.49239.2054
Wondimu, Getu Mekonnen, Dinka, Tekle Gemechu, Woldaregay, Mesfin, Duressa, Gemechis File. (1402). 'Fitted mesh numerical scheme for singularly perturbed delay reaction diffusion problem with integral boundary condition', سامانه مدیریت نشریات علمی, 11(3), pp. 478-494. doi: 10.22034/cmde.2023.49239.2054
Wondimu, Getu Mekonnen, Dinka, Tekle Gemechu, Woldaregay, Mesfin, Duressa, Gemechis File. Fitted mesh numerical scheme for singularly perturbed delay reaction diffusion problem with integral boundary condition. سامانه مدیریت نشریات علمی, 1402; 11(3): 478-494. doi: 10.22034/cmde.2023.49239.2054

Fitted mesh numerical scheme for singularly perturbed delay reaction diffusion problem with integral boundary condition

Computational Methods for Differential Equations
مقاله 4، دوره 11، شماره 3، شهریور 2023، صفحه 478-494    اصل مقاله (755.12 K)
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 Duressa2
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 plane. 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 nearly two orders of convergence in space and two orders of convergence 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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