Numerical method for solving fractional Sturm–Liouville eigenvalue problems of order two using Genocchi polynomials
A new numerical scheme based on Genocchi polynomials is constructed to solve fractional Sturm–Liouville problems of order two in which the fractional derivative is considered in the Caputo sense. First, the differen-tial equation with boundary conditions is converted into the corresponding integral...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Ferdowsi University of Mashhad
2023-03-01
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| Series: | Iranian Journal of Numerical Analysis and Optimization |
| Subjects: | |
| Online Access: | https://ijnao.um.ac.ir/article_42496_0bc74e05f3d8e7fabd81e3190409d004.pdf |
| _version_ | 1811158692478844928 |
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| author | A. Aghazadeh Y. Mahmoudi F. Dastmalchi Saei |
| author_facet | A. Aghazadeh Y. Mahmoudi F. Dastmalchi Saei |
| author_sort | A. Aghazadeh |
| collection | DOAJ |
| description | A new numerical scheme based on Genocchi polynomials is constructed to solve fractional Sturm–Liouville problems of order two in which the fractional derivative is considered in the Caputo sense. First, the differen-tial equation with boundary conditions is converted into the corresponding integral equation form. Next, the fractional integration and derivation op-erational matrices for Genocchi polynomials, are introduced and applied for approximating the eigenvalues of the problem. Then, the proposed polynomials are applied to approximate the corresponding eigenfunctions. Finally, some examples are presented to illustrate the efficiency and accu-racy of the numerical method. The results show that the proposed method is better than some other approximations involving orthogonal bases. |
| first_indexed | 2024-04-10T05:28:26Z |
| format | Article |
| id | doaj.art-d8e3aee966ad4ec09faec46f6bebc376 |
| institution | Directory Open Access Journal |
| issn | 2423-6977 2423-6969 |
| language | English |
| last_indexed | 2024-04-10T05:28:26Z |
| publishDate | 2023-03-01 |
| publisher | Ferdowsi University of Mashhad |
| record_format | Article |
| series | Iranian Journal of Numerical Analysis and Optimization |
| spelling | doaj.art-d8e3aee966ad4ec09faec46f6bebc3762023-03-07T09:30:31ZengFerdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-69772423-69692023-03-0113112114010.22067/ijnao.2022.75635.111542496Numerical method for solving fractional Sturm–Liouville eigenvalue problems of order two using Genocchi polynomialsA. Aghazadeh0Y. Mahmoudi1F. Dastmalchi Saei2Department of Mathematics, Tabriz Branch, Islamic Azad University, Tabriz, Iran.Department of Mathematics, Tabriz Branch, Islamic Azad University, Tabriz, Iran.Department of Mathematics, Tabriz Branch, Islamic Azad University, Tabriz, Iran.A new numerical scheme based on Genocchi polynomials is constructed to solve fractional Sturm–Liouville problems of order two in which the fractional derivative is considered in the Caputo sense. First, the differen-tial equation with boundary conditions is converted into the corresponding integral equation form. Next, the fractional integration and derivation op-erational matrices for Genocchi polynomials, are introduced and applied for approximating the eigenvalues of the problem. Then, the proposed polynomials are applied to approximate the corresponding eigenfunctions. Finally, some examples are presented to illustrate the efficiency and accu-racy of the numerical method. The results show that the proposed method is better than some other approximations involving orthogonal bases.https://ijnao.um.ac.ir/article_42496_0bc74e05f3d8e7fabd81e3190409d004.pdfsturm–liouville problemcaputo fractional derivativeeigen-valueeigenfunctiongenocchi polynomials |
| spellingShingle | A. Aghazadeh Y. Mahmoudi F. Dastmalchi Saei Numerical method for solving fractional Sturm–Liouville eigenvalue problems of order two using Genocchi polynomials Iranian Journal of Numerical Analysis and Optimization sturm–liouville problem caputo fractional derivative eigen-value eigenfunction genocchi polynomials |
| title | Numerical method for solving fractional Sturm–Liouville eigenvalue problems of order two using Genocchi polynomials |
| title_full | Numerical method for solving fractional Sturm–Liouville eigenvalue problems of order two using Genocchi polynomials |
| title_fullStr | Numerical method for solving fractional Sturm–Liouville eigenvalue problems of order two using Genocchi polynomials |
| title_full_unstemmed | Numerical method for solving fractional Sturm–Liouville eigenvalue problems of order two using Genocchi polynomials |
| title_short | Numerical method for solving fractional Sturm–Liouville eigenvalue problems of order two using Genocchi polynomials |
| title_sort | numerical method for solving fractional sturm liouville eigenvalue problems of order two using genocchi polynomials |
| topic | sturm–liouville problem caputo fractional derivative eigen-value eigenfunction genocchi polynomials |
| url | https://ijnao.um.ac.ir/article_42496_0bc74e05f3d8e7fabd81e3190409d004.pdf |
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