Modal Shifted Fifth-Kind Chebyshev Tau Integral Approach for Solving Heat Conduction Equation
In this study, a spectral tau solution to the heat conduction equation is introduced. As basis functions, the orthogonal polynomials, namely, the shifted fifth-kind Chebyshev polynomials (<i>5CPs</i>), are used. The proposed method’s derivation is based on solving the integral equation t...
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MDPI AG
2022-10-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/6/11/619 |
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| author | Ahmed Gamal Atta Waleed Mohamed Abd-Elhameed Galal Mahrous Moatimid Youssri Hassan Youssri |
| author_facet | Ahmed Gamal Atta Waleed Mohamed Abd-Elhameed Galal Mahrous Moatimid Youssri Hassan Youssri |
| author_sort | Ahmed Gamal Atta |
| collection | DOAJ |
| description | In this study, a spectral tau solution to the heat conduction equation is introduced. As basis functions, the orthogonal polynomials, namely, the shifted fifth-kind Chebyshev polynomials (<i>5CPs</i>), are used. The proposed method’s derivation is based on solving the integral equation that corresponds to the original problem. The tau approach and some theoretical findings serve to transform the problem with its underlying conditions into a suitable system of equations that can be successfully solved by the Gaussian elimination method. For the applicability and precision of our suggested algorithm, some numerical examples are given. |
| first_indexed | 2024-03-09T19:04:09Z |
| format | Article |
| id | doaj.art-100f4dfc08b544a583984b4faec6c404 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-09T19:04:09Z |
| publishDate | 2022-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-100f4dfc08b544a583984b4faec6c4042023-11-24T04:44:57ZengMDPI AGFractal and Fractional2504-31102022-10-0161161910.3390/fractalfract6110619Modal Shifted Fifth-Kind Chebyshev Tau Integral Approach for Solving Heat Conduction EquationAhmed Gamal Atta0Waleed Mohamed Abd-Elhameed1Galal Mahrous Moatimid2Youssri Hassan Youssri3Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo 11341, EgyptDepartment of Mathematics, Faculty of Science, Cairo University, Giza 12613, EgyptDepartment of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo 11341, EgyptDepartment of Mathematics, Faculty of Science, Cairo University, Giza 12613, EgyptIn this study, a spectral tau solution to the heat conduction equation is introduced. As basis functions, the orthogonal polynomials, namely, the shifted fifth-kind Chebyshev polynomials (<i>5CPs</i>), are used. The proposed method’s derivation is based on solving the integral equation that corresponds to the original problem. The tau approach and some theoretical findings serve to transform the problem with its underlying conditions into a suitable system of equations that can be successfully solved by the Gaussian elimination method. For the applicability and precision of our suggested algorithm, some numerical examples are given.https://www.mdpi.com/2504-3110/6/11/619heat conduction equationgeneralized hypergeometric functionsChebyshev polynomials of the fifth kindtau method |
| spellingShingle | Ahmed Gamal Atta Waleed Mohamed Abd-Elhameed Galal Mahrous Moatimid Youssri Hassan Youssri Modal Shifted Fifth-Kind Chebyshev Tau Integral Approach for Solving Heat Conduction Equation Fractal and Fractional heat conduction equation generalized hypergeometric functions Chebyshev polynomials of the fifth kind tau method |
| title | Modal Shifted Fifth-Kind Chebyshev Tau Integral Approach for Solving Heat Conduction Equation |
| title_full | Modal Shifted Fifth-Kind Chebyshev Tau Integral Approach for Solving Heat Conduction Equation |
| title_fullStr | Modal Shifted Fifth-Kind Chebyshev Tau Integral Approach for Solving Heat Conduction Equation |
| title_full_unstemmed | Modal Shifted Fifth-Kind Chebyshev Tau Integral Approach for Solving Heat Conduction Equation |
| title_short | Modal Shifted Fifth-Kind Chebyshev Tau Integral Approach for Solving Heat Conduction Equation |
| title_sort | modal shifted fifth kind chebyshev tau integral approach for solving heat conduction equation |
| topic | heat conduction equation generalized hypergeometric functions Chebyshev polynomials of the fifth kind tau method |
| url | https://www.mdpi.com/2504-3110/6/11/619 |
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