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Woldaregay, Mesfin Mekuria, Debela, Habtamu, Duressa, Gemechis File. (1401). Uniformly convergent fitted operator method for singularly perturbed delay differential equations. سامانه مدیریت نشریات علمی, 10(2), 502-518. doi: 10.22034/cmde.2021.41166.1789
Mesfin Mekuria Woldaregay; Habtamu Garoma Debela; Gemechis File Duressa. "Uniformly convergent fitted operator method for singularly perturbed delay differential equations". سامانه مدیریت نشریات علمی, 10, 2, 1401, 502-518. doi: 10.22034/cmde.2021.41166.1789
Woldaregay, Mesfin Mekuria, Debela, Habtamu, Duressa, Gemechis File. (1401). 'Uniformly convergent fitted operator method for singularly perturbed delay differential equations', سامانه مدیریت نشریات علمی, 10(2), pp. 502-518. doi: 10.22034/cmde.2021.41166.1789
Woldaregay, Mesfin Mekuria, Debela, Habtamu, Duressa, Gemechis File. Uniformly convergent fitted operator method for singularly perturbed delay differential equations. سامانه مدیریت نشریات علمی, 1401; 10(2): 502-518. doi: 10.22034/cmde.2021.41166.1789

Uniformly convergent fitted operator method for singularly perturbed delay differential equations

Computational Methods for Differential Equations
مقاله 16، دوره 10، شماره 2، تیر 2022، صفحه 502-518  XML اصل مقاله (203.06 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2021.41166.1789
نویسندگان
Mesfin Mekuria Woldaregay email orcid 1؛ Habtamu Garoma Debelaorcid 2؛ Gemechis File Duressa2
1Department of Applied Mathematics, Adama Science and Technology University, Adama, Ethiopia.
2Department of Mathematics, Jimma University, Jimma, Ethiopia.
چکیده
This paper deals with the numerical treatment of singularly perturbed delay differential equations having a delay on the first derivative term. The solution of the considered problem exhibits boundary layer behavior on the left or right side of the domain depending on the sign of the convective term. The term with the delay is approximated using Taylor series approximation, resulting in an asymptotically equivalent singularly perturbed boundary value problem. The uniformly convergent numerical scheme is developed using exponentially fitted finite difference method. The stability of the scheme is investigated using solution bound. The uniform convergence of the scheme is discussed and proved. Numerical examples are considered to validate the theoretical analysis. 
کلیدواژه‌ها
Fitted operator؛ Singularly perturbed problem؛ Uniform convergence
مراجع
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