Mixed Chebyshev and Legendre polynomials differentiation matrices for solving initial-boundary value problems
A new form of basis functions structures has been constructed. These basis functions constitute a mix of Chebyshev polynomials and Legendre polynomials. The main purpose of these structures is to present several forms of differentiation matrices. These matrices were built from the perspective of pse...
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AIMS Press
2023-08-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20231255?viewType=HTML |
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| author | Dina Abdelhamid Wedad Albalawi Kottakkaran Sooppy Nisar A. Abdel-Aty Suliman Alsaeed M. Abdelhakem |
| author_facet | Dina Abdelhamid Wedad Albalawi Kottakkaran Sooppy Nisar A. Abdel-Aty Suliman Alsaeed M. Abdelhakem |
| author_sort | Dina Abdelhamid |
| collection | DOAJ |
| description | A new form of basis functions structures has been constructed. These basis functions constitute a mix of Chebyshev polynomials and Legendre polynomials. The main purpose of these structures is to present several forms of differentiation matrices. These matrices were built from the perspective of pseudospectral approximation. Also, an investigation of the error analysis for the proposed expansion has been done. Then, we showed the presented matrices' efficiency and accuracy with several test functions. Consequently, the correctness of our matrices is demonstrated by solving ordinary differential equations and some initial boundary value problems. Finally, some comparisons between the presented approximations, exact solutions, and other methods ensured the efficiency and accuracy of the proposed matrices. |
| first_indexed | 2024-03-12T02:07:25Z |
| format | Article |
| id | doaj.art-a6dc0028ba774df2842abda4265f2010 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-12T02:07:25Z |
| publishDate | 2023-08-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-a6dc0028ba774df2842abda4265f20102023-09-07T01:45:10ZengAIMS PressAIMS Mathematics2473-69882023-08-01810246092463110.3934/math.20231255Mixed Chebyshev and Legendre polynomials differentiation matrices for solving initial-boundary value problemsDina Abdelhamid0Wedad Albalawi 1Kottakkaran Sooppy Nisar2A. Abdel-Aty3Suliman Alsaeed 4M. Abdelhakem 51. Basic Science Department, Faculty of Engineering, May University in Cairo, Cairo, Egypt8. Helwan School of Numerical Analysis in Egypt (HSNAE), Egypt2. Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia3. Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam bin Abdulaziz University, Al Kharj 11942, Saudi Arabia4. Department of Physics, College of Sciences, University of Bisha, P.O. Box 344, Bisha 61922, Saudi Arabia3. Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam bin Abdulaziz University, Al Kharj 11942, Saudi Arabia5. Applied Sciences College, Department of Mathematical Sciences, Umm Al-Qura University P.O. Box 715, Makkah 21955, Saudi Arabia6. Department of Mathematics, Faculty of Science, Helwan University, Cairo, Egypt 7. Basic Science Department, School of Engineering, Canadian International College (CIC), New Cairo, Egypt 8. Helwan School of Numerical Analysis in Egypt (HSNAE), EgyptA new form of basis functions structures has been constructed. These basis functions constitute a mix of Chebyshev polynomials and Legendre polynomials. The main purpose of these structures is to present several forms of differentiation matrices. These matrices were built from the perspective of pseudospectral approximation. Also, an investigation of the error analysis for the proposed expansion has been done. Then, we showed the presented matrices' efficiency and accuracy with several test functions. Consequently, the correctness of our matrices is demonstrated by solving ordinary differential equations and some initial boundary value problems. Finally, some comparisons between the presented approximations, exact solutions, and other methods ensured the efficiency and accuracy of the proposed matrices.https://www.aimspress.com/article/doi/10.3934/math.20231255?viewType=HTMLchebyshev polynomialslegendre polynomialspseudospectral differential matriceserror analysisibvpsricatti equation |
| spellingShingle | Dina Abdelhamid Wedad Albalawi Kottakkaran Sooppy Nisar A. Abdel-Aty Suliman Alsaeed M. Abdelhakem Mixed Chebyshev and Legendre polynomials differentiation matrices for solving initial-boundary value problems AIMS Mathematics chebyshev polynomials legendre polynomials pseudospectral differential matrices error analysis ibvps ricatti equation |
| title | Mixed Chebyshev and Legendre polynomials differentiation matrices for solving initial-boundary value problems |
| title_full | Mixed Chebyshev and Legendre polynomials differentiation matrices for solving initial-boundary value problems |
| title_fullStr | Mixed Chebyshev and Legendre polynomials differentiation matrices for solving initial-boundary value problems |
| title_full_unstemmed | Mixed Chebyshev and Legendre polynomials differentiation matrices for solving initial-boundary value problems |
| title_short | Mixed Chebyshev and Legendre polynomials differentiation matrices for solving initial-boundary value problems |
| title_sort | mixed chebyshev and legendre polynomials differentiation matrices for solving initial boundary value problems |
| topic | chebyshev polynomials legendre polynomials pseudospectral differential matrices error analysis ibvps ricatti equation |
| url | https://www.aimspress.com/article/doi/10.3934/math.20231255?viewType=HTML |
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