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 |
| Veröffentlicht: |
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 |
| Завантажити файл: | |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | 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. |
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| DOI: | 10.3842/umzh.v76i1.7331 |