A fitted approximate method for solving singularly perturbed Volterra–Fredholm integro-differential equations with an integral boundary condition
UDC 517.9 We consider a novel numerical approach for solving boundary-value problems for the second-order Volterra–Fredholm integro-differential equation with layer behavior and an integral boundary condition. A finite-difference scheme is proposed on suitable Shishkin-type mesh to obta...
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| Datum: | 2024 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Institute of Mathematics, NAS of Ukraine
2024
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/7331 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1865793896929296384 |
|---|---|
| author | Gunes, Baransel Cakir, Musa Gunes, Baransel Cakir, Musa |
| author_facet | Gunes, Baransel Cakir, Musa Gunes, Baransel Cakir, Musa |
| author_institution_txt_mv | [
{
"author": "Baransel Gunes",
"institution": "Department of Mathematics, Faculty of Science, Van Yuzuncu Yil University, Turkey"
},
{
"author": "Musa Cakir",
"institution": "Department of Mathematics, Faculty of Science, Van Yuzuncu Yil University, Turkey"
}
] |
| author_sort | Gunes, Baransel |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2024-06-19T00:35:03Z |
| description | UDC 517.9
We consider a novel numerical approach for solving boundary-value problems for the second-order Volterra–Fredholm integro-differential equation with layer behavior and an integral boundary condition. A finite-difference scheme is proposed on suitable Shishkin-type mesh to obtain the approximate solution of the presented problem. It is proven that the method is first-order convergent in the discrete maximum norm. Two numerical examples are included to show the efficiency of the method. |
| doi_str_mv | 10.3842/umzh.v76i1.7331 |
| first_indexed | 2026-03-24T03:32:19Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-7331 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:32:19Z |
| publishDate | 2024 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-73312024-06-19T00:35:03Z A fitted approximate method for solving singularly perturbed Volterra–Fredholm integro-differential equations with an integral boundary condition A fitted approximate method for solving singularly perturbed Volterra–Fredholm integro-differential equations with an integral boundary condition Gunes, Baransel Cakir, Musa Gunes, Baransel Cakir, Musa Finite difference method integral boundary condition integro-differential equation singular perturbation uniform convergence Numerical Analysis Singularly Perturbed Problems Finite Difference Scheme Integro-Differential Equation UDC 517.9 We consider a novel numerical approach for solving boundary-value problems for the second-order Volterra–Fredholm integro-differential equation with layer behavior and an integral boundary condition. A finite-difference scheme is proposed on suitable Shishkin-type mesh to obtain the approximate solution of the presented problem. It is proven that the method is first-order convergent in the discrete maximum norm. Two numerical examples are included to show the efficiency of the method. УДК 517.9 Підігнаний наближений метод розв'язування сингулярно збурених інтегро-диференціальних рівнянь Вольтерра–Фредгольма з інтегральною крайовою умовою Розглянуто новий числовий підхід до розв'язування крайових задач для інтегро-диференціального рівняння Вольтерра–Фредгольма другого порядку з поведінкою шару та інтегральною граничною умовою. Запропоновано скінчен\-но-різницеву схему на відповідній сітці типу Шишкіна для отримання наближеного розв'язку поставленої задачі. Доведено, що запропонований метод є збіжним першого порядку за дискретною максимальною нормою. Наведено два числових приклади, що демонструють ефективність цього методу. Institute of Mathematics, NAS of Ukraine 2024-02-02 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/7331 10.3842/umzh.v76i1.7331 Ukrains’kyi Matematychnyi Zhurnal; Vol. 76 No. 1 (2024); 115 - 131 Український математичний журнал; Том 76 № 1 (2024); 115 - 131 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/7331/9683 Copyright (c) 2024 Baransel Gunes, Musa Cakir |
| spellingShingle | Gunes, Baransel Cakir, Musa Gunes, Baransel Cakir, Musa A fitted approximate method for solving singularly perturbed Volterra–Fredholm integro-differential equations with an integral boundary condition |
| title | A fitted approximate method for solving singularly perturbed Volterra–Fredholm integro-differential equations with an integral boundary condition |
| title_alt | A fitted approximate method for solving singularly perturbed Volterra–Fredholm integro-differential equations with an integral boundary condition |
| title_full | A fitted approximate method for solving singularly perturbed Volterra–Fredholm integro-differential equations with an integral boundary condition |
| title_fullStr | A fitted approximate method for solving singularly perturbed Volterra–Fredholm integro-differential equations with an integral boundary condition |
| title_full_unstemmed | A fitted approximate method for solving singularly perturbed Volterra–Fredholm integro-differential equations with an integral boundary condition |
| title_short | A fitted approximate method for solving singularly perturbed Volterra–Fredholm integro-differential equations with an integral boundary condition |
| title_sort | fitted approximate method for solving singularly perturbed volterra–fredholm integro-differential equations with an integral boundary condition |
| topic_facet | Finite difference method integral boundary condition integro-differential equation singular perturbation uniform convergence Numerical Analysis Singularly Perturbed Problems Finite Difference Scheme Integro-Differential Equation |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/7331 |
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