Legendre spectral collocation method for solving nonlinear fractional Fredholm integro-differential equations with convergence analysis
The main purpose of this work was to develop a spectrally accurate collocation method for solving nonlinear fractional Fredholm integro-differential equations (non-FFIDEs). A proposed spectral collocation method is based on the Legendre-Gauss-Lobatto collocation (L-G-LC) method in which the main ide...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-02-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2024388?viewType=HTML |
| _version_ | 1797277592915542016 |
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| author | A. H. Tedjani A. Z. Amin Abdel-Haleem Abdel-Aty M. A. Abdelkawy Mona Mahmoud |
| author_facet | A. H. Tedjani A. Z. Amin Abdel-Haleem Abdel-Aty M. A. Abdelkawy Mona Mahmoud |
| author_sort | A. H. Tedjani |
| collection | DOAJ |
| description | The main purpose of this work was to develop a spectrally accurate collocation method for solving nonlinear fractional Fredholm integro-differential equations (non-FFIDEs). A proposed spectral collocation method is based on the Legendre-Gauss-Lobatto collocation (L-G-LC) method in which the main idea is to use Caputo derivatives and Legendre-Gauss interpolation for nonlinear FFIDEs. A rigorous convergence analysis is provided and confirmed by numerical tests. In addition, we provide some numerical test cases to demonstrate that the approach can preserve the non-smooth solution of the underlying problem. |
| first_indexed | 2024-03-07T15:51:41Z |
| format | Article |
| id | doaj.art-bfb5183dc5db450a8d02d197cd07e0e8 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-07T15:51:41Z |
| publishDate | 2024-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-bfb5183dc5db450a8d02d197cd07e0e82024-03-05T01:31:10ZengAIMS PressAIMS Mathematics2473-69882024-02-01947973800010.3934/math.2024388Legendre spectral collocation method for solving nonlinear fractional Fredholm integro-differential equations with convergence analysisA. H. Tedjani 0A. Z. Amin1Abdel-Haleem Abdel-Aty2M. A. Abdelkawy3Mona Mahmoud41. Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia2. Department of Mathematical Sciences, Faculty of Science & Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor, Malaysia3. Department of Physics, College of Sciences, University of Bisha, P.O. Box 344, Bisha 61922, Saudi Arabia1. Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia4. Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt5. Department of Physics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi ArabiaThe main purpose of this work was to develop a spectrally accurate collocation method for solving nonlinear fractional Fredholm integro-differential equations (non-FFIDEs). A proposed spectral collocation method is based on the Legendre-Gauss-Lobatto collocation (L-G-LC) method in which the main idea is to use Caputo derivatives and Legendre-Gauss interpolation for nonlinear FFIDEs. A rigorous convergence analysis is provided and confirmed by numerical tests. In addition, we provide some numerical test cases to demonstrate that the approach can preserve the non-smooth solution of the underlying problem.https://www.aimspress.com/article/doi/10.3934/math.2024388?viewType=HTMLlegendre-gauss-lobattofractional fredholm integro-differential equationcaputo fractional derivativeconvergence analysisspectral method |
| spellingShingle | A. H. Tedjani A. Z. Amin Abdel-Haleem Abdel-Aty M. A. Abdelkawy Mona Mahmoud Legendre spectral collocation method for solving nonlinear fractional Fredholm integro-differential equations with convergence analysis AIMS Mathematics legendre-gauss-lobatto fractional fredholm integro-differential equation caputo fractional derivative convergence analysis spectral method |
| title | Legendre spectral collocation method for solving nonlinear fractional Fredholm integro-differential equations with convergence analysis |
| title_full | Legendre spectral collocation method for solving nonlinear fractional Fredholm integro-differential equations with convergence analysis |
| title_fullStr | Legendre spectral collocation method for solving nonlinear fractional Fredholm integro-differential equations with convergence analysis |
| title_full_unstemmed | Legendre spectral collocation method for solving nonlinear fractional Fredholm integro-differential equations with convergence analysis |
| title_short | Legendre spectral collocation method for solving nonlinear fractional Fredholm integro-differential equations with convergence analysis |
| title_sort | legendre spectral collocation method for solving nonlinear fractional fredholm integro differential equations with convergence analysis |
| topic | legendre-gauss-lobatto fractional fredholm integro-differential equation caputo fractional derivative convergence analysis spectral method |
| url | https://www.aimspress.com/article/doi/10.3934/math.2024388?viewType=HTML |
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