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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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Дата:2024
Автори: Gunes, Baransel, Cakir, Musa
Формат: Стаття
Мова:Англійська
Опубліковано: Institute of Mathematics, NAS of Ukraine 2024
Онлайн доступ: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
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author Gunes, Baransel
Cakir, Musa
Gunes, Baransel
Cakir, Musa
author_facet Gunes, Baransel
Cakir, Musa
Gunes, Baransel
Cakir, Musa
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 Skip to main content Advertisement Log in Menu Find a journal Publish with us Track your research Search Saved research Cart Home Ukrainian Mathematical Journal Article A Fitted Approximate Method for Solving Singularly Perturbed Volterra–Fredholm Integrodifferential Equations with Integral Boundary Condition Published: 30 July 2024 Volume 76, pages 122–140, (2024) Cite this article Save article View saved research Ukrainian Mathematical Journal Aims and scope Submit manuscript Baransel Gunes1 & Musa Cakir1  147 Accesses 1 Citation Explore all metrics We consider a novel numerical approach for solving boundary-value problems for the second-order Volterra-Fredholm integrodifferential equation with layer behavior and an integral boundary condition. A finite-difference scheme is proposed on suitable Shishkin-type mesh to obtain an approximate solution of the presented problem. It is proved that the method is first-order convergent in the discrete maximum norm. Two numerical examples are included to show the efficiency of the method. This is a preview of subscription content, log in via an institution to check access. Access this article Log in via an institution Subscribe and save Springer+ from €37.37 /Month Starting from 10 chapters or articles per month Access and download chapters and articles from more than 300k books and 2,500 journals Cancel anytime View plans Buy Now Buy article PDF 39,95 € Price includes VAT (Ukraine) Instant access to the full article PDF. Institutional subscriptions Similar content being viewed by others A numerical approach for singularly perturbed reaction diffusion type Volterra-Fredholm integro-differential equations Article 12 July 2023 An efficient numerical method for a singularly perturbed Fredholm integro-differential equation with integral boundary condition Article 09 June 2022 Numerical scheme for singularly perturbed Fredholm integro-differential equations with non-local boundary conditions Article 24 March 2024 Explore related subjects Discover the latest articles, books and news in related subjects, suggested using machine learning. Differential Equations Integral Equations Numerical Analysis Ordinary Differential Equations Partial Differential Equations Stochastic Integral Equations Fractional Differential Equations and Numerical Methods References N. Adzic, “Spectral approximation and nonlocal boundary value problems,” Novi Sad J. Math., 30, 1–10 (2000). MathSciNet  Google Scholar  G. M. 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Additional information Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 76, No. 1, pp. 115–131, January, 2024. Ukrainian DOI: https://doi.org/10.3842/umzh.v76i1.7331. Rights and permissions Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Reprints and permissions About this article Cite this article Gunes, B., Cakir, M. A Fitted Approximate Method for Solving Singularly Perturbed Volterra–Fredholm Integrodifferential Equations with Integral Boundary Condition. Ukr Math J 76, 122–140 (2024). https://doi.org/10.1007/s11253-024-02312-z Download citation Received: 27 September 2022 Published: 30 July 2024 Version of record: 30 July 2024 Issue date: June 2024 DOI: https://doi.org/10.1007/s11253-024-02312-z Share this article Anyone you share the following link with will be able to read this content: Get shareable linkSorry, a shareable link is not currently available for this article. Copy shareable link to clipboard Provided by the Springer Nature SharedIt content-sharing initiative Access this article Log in via an institution Subscribe and save Springer+ from €37.37 /Month Starting from 10 chapters or articles per month Access and download chapters and articles from more than 300k books and 2,500 journals Cancel anytime View plans Buy Now Buy article PDF 39,95 € Price includes VAT (Ukraine) Instant access to the full article PDF. 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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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