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Block-by-block method for solving non-linear Volterra integral equation of the first kind

In this paper, we focus on the numerical solution of the non-linear Volterra integral equation of the first kind. We start by converting its form to a second-kind Volterra equation and we construct some assumptions to give a sufficient condition to ensure the solution’s existence and uniqueness, thi...

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Autores principales: Ghiat, Mourad, Tair, Boutheina, Ghuebbai, Hamza, Kamouche, Soumia
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2023
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9893989/
http://dx.doi.org/10.1007/s40314-023-02212-1
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author Ghiat, Mourad
Tair, Boutheina
Ghuebbai, Hamza
Kamouche, Soumia
author_facet Ghiat, Mourad
Tair, Boutheina
Ghuebbai, Hamza
Kamouche, Soumia
author_sort Ghiat, Mourad
collection PubMed
description In this paper, we focus on the numerical solution of the non-linear Volterra integral equation of the first kind. We start by converting its form to a second-kind Volterra equation and we construct some assumptions to give a sufficient condition to ensure the solution’s existence and uniqueness, this is on the one hand. On the other hand, to use it in the numerical and analytical analysis computation which put the two analyses compatible. Then, by applying block-by-block method, we transform our integral equation to a non-linear system. This system gives us a discrete numerical solution converging to our analytical solution. The approximate solution is computed using a Newton’s method and the numerical examples clearly demonstrate the efficiency of our proposed method compared with the Nystöm method.
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spelling pubmed-98939892023-02-02 Block-by-block method for solving non-linear Volterra integral equation of the first kind Ghiat, Mourad Tair, Boutheina Ghuebbai, Hamza Kamouche, Soumia Comp. Appl. Math. Article In this paper, we focus on the numerical solution of the non-linear Volterra integral equation of the first kind. We start by converting its form to a second-kind Volterra equation and we construct some assumptions to give a sufficient condition to ensure the solution’s existence and uniqueness, this is on the one hand. On the other hand, to use it in the numerical and analytical analysis computation which put the two analyses compatible. Then, by applying block-by-block method, we transform our integral equation to a non-linear system. This system gives us a discrete numerical solution converging to our analytical solution. The approximate solution is computed using a Newton’s method and the numerical examples clearly demonstrate the efficiency of our proposed method compared with the Nystöm method. Springer International Publishing 2023-02-02 2023 /pmc/articles/PMC9893989/ http://dx.doi.org/10.1007/s40314-023-02212-1 Text en © The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional 2023, 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. This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic.
spellingShingle Article
Ghiat, Mourad
Tair, Boutheina
Ghuebbai, Hamza
Kamouche, Soumia
Block-by-block method for solving non-linear Volterra integral equation of the first kind
title Block-by-block method for solving non-linear Volterra integral equation of the first kind
title_full Block-by-block method for solving non-linear Volterra integral equation of the first kind
title_fullStr Block-by-block method for solving non-linear Volterra integral equation of the first kind
title_full_unstemmed Block-by-block method for solving non-linear Volterra integral equation of the first kind
title_short Block-by-block method for solving non-linear Volterra integral equation of the first kind
title_sort block-by-block method for solving non-linear volterra integral equation of the first kind
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9893989/
http://dx.doi.org/10.1007/s40314-023-02212-1
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