Legendre Superconvergent Degenerate Kernel and Nystrom Methods for Fredholm Integral Equations
In this paper, polynomial-based superconvergent degenerate kernel and {Nyström} methods for solving {Fredholm} integral equations of the second kind with the smooth kernel are studied. By using an interpolatory projection based on Legendre polynomials of degree $\leq n,$ we analyze the convergence...
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| Format: | Article |
| Language: | English |
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University of Maragheh
2023-01-01
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| Series: | Sahand Communications in Mathematical Analysis |
| Subjects: | |
| Online Access: | https://scma.maragheh.ac.ir/article_697066_b68704048e05e11170c69878b2856126.pdf |
| _version_ | 1811175411591151616 |
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| author | Bouda Hamza Allouch Chafik Tahrichi Mohamed |
| author_facet | Bouda Hamza Allouch Chafik Tahrichi Mohamed |
| author_sort | Bouda Hamza |
| collection | DOAJ |
| description | In this paper, polynomial-based superconvergent degenerate kernel and {Nyström} methods for solving {Fredholm} integral equations of the second kind with the smooth kernel are studied. By using an interpolatory projection based on Legendre polynomials of degree $\leq n,$ we analyze the convergence of these methods and we establish superconvergence results for their iterated versions. Two numerical examples are given to illustrate the theoretical estimates. |
| first_indexed | 2024-04-10T19:35:44Z |
| format | Article |
| id | doaj.art-96c1a645870a413189005003a9a89137 |
| institution | Directory Open Access Journal |
| issn | 2322-5807 2423-3900 |
| language | English |
| last_indexed | 2024-04-10T19:35:44Z |
| publishDate | 2023-01-01 |
| publisher | University of Maragheh |
| record_format | Article |
| series | Sahand Communications in Mathematical Analysis |
| spelling | doaj.art-96c1a645870a413189005003a9a891372023-01-30T06:10:45ZengUniversity of MaraghehSahand Communications in Mathematical Analysis2322-58072423-39002023-01-01201456010.22130/scma.2022.550563.1078697066Legendre Superconvergent Degenerate Kernel and Nystrom Methods for Fredholm Integral EquationsBouda Hamza0Allouch Chafik1Tahrichi Mohamed2University Mohammed I, Team MSC, FPN, LAMAO Laboratory, Nador, 62000, Morocco.University Mohammed I, Team MSC, FPN, LAMAO Laboratory, Nador, 62000, Morocco.University Mohammed I, Team ANAA, EST, LANO Laboratory, Oujda, 60000, Morocco.In this paper, polynomial-based superconvergent degenerate kernel and {Nyström} methods for solving {Fredholm} integral equations of the second kind with the smooth kernel are studied. By using an interpolatory projection based on Legendre polynomials of degree $\leq n,$ we analyze the convergence of these methods and we establish superconvergence results for their iterated versions. Two numerical examples are given to illustrate the theoretical estimates.https://scma.maragheh.ac.ir/article_697066_b68704048e05e11170c69878b2856126.pdffredholm integral equationsdegenerate kernel and nystr¨om methodslegendre polynomialsinterpolatory projectionsuperconvergence rates |
| spellingShingle | Bouda Hamza Allouch Chafik Tahrichi Mohamed Legendre Superconvergent Degenerate Kernel and Nystrom Methods for Fredholm Integral Equations Sahand Communications in Mathematical Analysis fredholm integral equations degenerate kernel and nystr¨om methods legendre polynomials interpolatory projection superconvergence rates |
| title | Legendre Superconvergent Degenerate Kernel and Nystrom Methods for Fredholm Integral Equations |
| title_full | Legendre Superconvergent Degenerate Kernel and Nystrom Methods for Fredholm Integral Equations |
| title_fullStr | Legendre Superconvergent Degenerate Kernel and Nystrom Methods for Fredholm Integral Equations |
| title_full_unstemmed | Legendre Superconvergent Degenerate Kernel and Nystrom Methods for Fredholm Integral Equations |
| title_short | Legendre Superconvergent Degenerate Kernel and Nystrom Methods for Fredholm Integral Equations |
| title_sort | legendre superconvergent degenerate kernel and nystrom methods for fredholm integral equations |
| topic | fredholm integral equations degenerate kernel and nystr¨om methods legendre polynomials interpolatory projection superconvergence rates |
| url | https://scma.maragheh.ac.ir/article_697066_b68704048e05e11170c69878b2856126.pdf |
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