Spectral approximation methods for Fredholm integral equations with non-smooth kernels
In this paper, polynomially based projection and modified projection methods for approximating the solution of Fredholm integral equations with a kernel of Green’s function type are studied. The projection is either an orthogonal projection or an interpolatory projection using Legendre polynomial b...
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| Format: | Article |
| Language: | English |
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Vilnius Gediminas Technical University
2022-11-01
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| Series: | Mathematical Modelling and Analysis |
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| Online Access: | https://journals.vilniustech.lt/index.php/MMA/article/view/16029 |
| _version_ | 1797984327227670528 |
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| author | Chafik Allouch Driss Sbibih Mohamed Tahrichi |
| author_facet | Chafik Allouch Driss Sbibih Mohamed Tahrichi |
| author_sort | Chafik Allouch |
| collection | DOAJ |
| description |
In this paper, polynomially based projection and modified projection methods for approximating the solution of Fredholm integral equations with a kernel of Green’s function type are studied. The projection is either an orthogonal projection or an interpolatory projection using Legendre polynomial basis. The orders of convergence of these methods and those of superconvergence of the iterated versions are analysed. A numerical example is given to illustrate the theoretical results.
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| first_indexed | 2024-04-11T07:00:08Z |
| format | Article |
| id | doaj.art-7ff7b569c8e740ddb90dc784a902f452 |
| institution | Directory Open Access Journal |
| issn | 1392-6292 1648-3510 |
| language | English |
| last_indexed | 2024-04-11T07:00:08Z |
| publishDate | 2022-11-01 |
| publisher | Vilnius Gediminas Technical University |
| record_format | Article |
| series | Mathematical Modelling and Analysis |
| spelling | doaj.art-7ff7b569c8e740ddb90dc784a902f4522022-12-22T04:38:48ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102022-11-0127410.3846/mma.2022.16029Spectral approximation methods for Fredholm integral equations with non-smooth kernelsChafik Allouch0Driss Sbibih1Mohamed Tahrichi2The Multidisciplinary Faculty of Nador, Team MSC, LAMAO Laboratory, Nador, MoroccoUniversity Mohammed I, FSO, LANO Laboratory, Oujda, MoroccoUniversity Mohammed I, Team ANAA, EST, LANO Laboratory, Oujda, Morocco In this paper, polynomially based projection and modified projection methods for approximating the solution of Fredholm integral equations with a kernel of Green’s function type are studied. The projection is either an orthogonal projection or an interpolatory projection using Legendre polynomial basis. The orders of convergence of these methods and those of superconvergence of the iterated versions are analysed. A numerical example is given to illustrate the theoretical results. https://journals.vilniustech.lt/index.php/MMA/article/view/16029Fredholm integral equationorthogonal projectioninterpolatory projectionLegendre polynomialsuperconvergence |
| spellingShingle | Chafik Allouch Driss Sbibih Mohamed Tahrichi Spectral approximation methods for Fredholm integral equations with non-smooth kernels Mathematical Modelling and Analysis Fredholm integral equation orthogonal projection interpolatory projection Legendre polynomial superconvergence |
| title | Spectral approximation methods for Fredholm integral equations with non-smooth kernels |
| title_full | Spectral approximation methods for Fredholm integral equations with non-smooth kernels |
| title_fullStr | Spectral approximation methods for Fredholm integral equations with non-smooth kernels |
| title_full_unstemmed | Spectral approximation methods for Fredholm integral equations with non-smooth kernels |
| title_short | Spectral approximation methods for Fredholm integral equations with non-smooth kernels |
| title_sort | spectral approximation methods for fredholm integral equations with non smooth kernels |
| topic | Fredholm integral equation orthogonal projection interpolatory projection Legendre polynomial superconvergence |
| url | https://journals.vilniustech.lt/index.php/MMA/article/view/16029 |
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