Generalized third-kind Chebyshev tau approach for treating the time fractional cable problem
This work introduces a computational method for solving the time-fractional cable equation (TFCE). We utilize the tau method for the numerical treatment of the TFCE, using generalized Chebyshev polynomials of the third kind (GCPs3) as basis functions. The integer and fractional derivatives of the GC...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-11-01
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| Series: | Electronic Research Archive |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2024288 |
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| author | Waleed Mohamed Abd-Elhameed Omar Mazen Alqubori Abdulrahman Khalid Al-Harbi Mohammed H. Alharbi Ahmed Gamal Atta |
| author_facet | Waleed Mohamed Abd-Elhameed Omar Mazen Alqubori Abdulrahman Khalid Al-Harbi Mohammed H. Alharbi Ahmed Gamal Atta |
| author_sort | Waleed Mohamed Abd-Elhameed |
| collection | DOAJ |
| description | This work introduces a computational method for solving the time-fractional cable equation (TFCE). We utilize the tau method for the numerical treatment of the TFCE, using generalized Chebyshev polynomials of the third kind (GCPs3) as basis functions. The integer and fractional derivatives of the GCPs3 are the essential formulas that serve to transform the TFCE with its underlying conditions into a matrix system. This system can be solved using a suitable algorithm to obtain the desired approximate solutions. The error bound resulting from the approximation by the proposed method is given. The numerical algorithm has been validated against existing methods by presenting numerical examples. |
| format | Article |
| id | doaj-art-88f6e48d8e7041e7ab15d455c97e204d |
| institution | Kabale University |
| issn | 2688-1594 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Electronic Research Archive |
| spelling | doaj-art-88f6e48d8e7041e7ab15d455c97e204d2025-01-23T07:53:00ZengAIMS PressElectronic Research Archive2688-15942024-11-0132116200622410.3934/era.2024288Generalized third-kind Chebyshev tau approach for treating the time fractional cable problemWaleed Mohamed Abd-Elhameed0Omar Mazen Alqubori1Abdulrahman Khalid Al-Harbi2Mohammed H. Alharbi3Ahmed Gamal Atta4Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, EgyptDepartment of Mathematics and Statistics, College of Science, University of Jeddah, Jeddah, Saudi ArabiaDepartment of Mathematics and Statistics, College of Science, University of Jeddah, Jeddah, Saudi ArabiaDepartment of Mathematics and Statistics, College of Science, University of Jeddah, Jeddah, Saudi ArabiaDepartment of Mathematics, Faculty of Education, Ain Shams University, Roxy 11341, Cairo, EgyptThis work introduces a computational method for solving the time-fractional cable equation (TFCE). We utilize the tau method for the numerical treatment of the TFCE, using generalized Chebyshev polynomials of the third kind (GCPs3) as basis functions. The integer and fractional derivatives of the GCPs3 are the essential formulas that serve to transform the TFCE with its underlying conditions into a matrix system. This system can be solved using a suitable algorithm to obtain the desired approximate solutions. The error bound resulting from the approximation by the proposed method is given. The numerical algorithm has been validated against existing methods by presenting numerical examples.https://www.aimspress.com/article/doi/10.3934/era.2024288chebyshev polynomialsjacobi polynomialsspectral methodsmatrix systemconvergence analysis |
| spellingShingle | Waleed Mohamed Abd-Elhameed Omar Mazen Alqubori Abdulrahman Khalid Al-Harbi Mohammed H. Alharbi Ahmed Gamal Atta Generalized third-kind Chebyshev tau approach for treating the time fractional cable problem Electronic Research Archive chebyshev polynomials jacobi polynomials spectral methods matrix system convergence analysis |
| title | Generalized third-kind Chebyshev tau approach for treating the time fractional cable problem |
| title_full | Generalized third-kind Chebyshev tau approach for treating the time fractional cable problem |
| title_fullStr | Generalized third-kind Chebyshev tau approach for treating the time fractional cable problem |
| title_full_unstemmed | Generalized third-kind Chebyshev tau approach for treating the time fractional cable problem |
| title_short | Generalized third-kind Chebyshev tau approach for treating the time fractional cable problem |
| title_sort | generalized third kind chebyshev tau approach for treating the time fractional cable problem |
| topic | chebyshev polynomials jacobi polynomials spectral methods matrix system convergence analysis |
| url | https://www.aimspress.com/article/doi/10.3934/era.2024288 |
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