Pseudospectral Method Based on Müntz–Legendre Wavelets for Solving the Abel Integral Equation
This paper deals with the numerical solution of the Abel integral equation based on Müntz–Legendre wavelets. To this end, the Abel integral operator is represented by Müntz–Legendre wavelets as an operational matrix. To find this matrix, we use the similarity between the Abel integral operator and t...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/2251623 |
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| _version_ | 1850216146346704896 |
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| author | Ioannis Dassios Fairouz Tchier F. M. O. Tawfiq |
| author_facet | Ioannis Dassios Fairouz Tchier F. M. O. Tawfiq |
| author_sort | Ioannis Dassios |
| collection | DOAJ |
| description | This paper deals with the numerical solution of the Abel integral equation based on Müntz–Legendre wavelets. To this end, the Abel integral operator is represented by Müntz–Legendre wavelets as an operational matrix. To find this matrix, we use the similarity between the Abel integral operator and the fractional integral operator. The proposed method can be easily used to solve weakly singular Volterra integral equations. We have proved the convergence of the proposed method. To demonstrate the ability and accuracy of the method, some numerical examples are presented. |
| format | Article |
| id | doaj-art-419f6a99de614f4d8c1654356fa4a2d7 |
| institution | OA Journals |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-419f6a99de614f4d8c1654356fa4a2d72025-08-20T02:08:24ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/2251623Pseudospectral Method Based on Müntz–Legendre Wavelets for Solving the Abel Integral EquationIoannis Dassios0Fairouz Tchier1F. M. O. Tawfiq2AMPSASDepartment of MathematicsDepartment of MathematicsThis paper deals with the numerical solution of the Abel integral equation based on Müntz–Legendre wavelets. To this end, the Abel integral operator is represented by Müntz–Legendre wavelets as an operational matrix. To find this matrix, we use the similarity between the Abel integral operator and the fractional integral operator. The proposed method can be easily used to solve weakly singular Volterra integral equations. We have proved the convergence of the proposed method. To demonstrate the ability and accuracy of the method, some numerical examples are presented.http://dx.doi.org/10.1155/2022/2251623 |
| spellingShingle | Ioannis Dassios Fairouz Tchier F. M. O. Tawfiq Pseudospectral Method Based on Müntz–Legendre Wavelets for Solving the Abel Integral Equation Journal of Mathematics |
| title | Pseudospectral Method Based on Müntz–Legendre Wavelets for Solving the Abel Integral Equation |
| title_full | Pseudospectral Method Based on Müntz–Legendre Wavelets for Solving the Abel Integral Equation |
| title_fullStr | Pseudospectral Method Based on Müntz–Legendre Wavelets for Solving the Abel Integral Equation |
| title_full_unstemmed | Pseudospectral Method Based on Müntz–Legendre Wavelets for Solving the Abel Integral Equation |
| title_short | Pseudospectral Method Based on Müntz–Legendre Wavelets for Solving the Abel Integral Equation |
| title_sort | pseudospectral method based on muntz legendre wavelets for solving the abel integral equation |
| url | http://dx.doi.org/10.1155/2022/2251623 |
| work_keys_str_mv | AT ioannisdassios pseudospectralmethodbasedonmuntzlegendrewaveletsforsolvingtheabelintegralequation AT fairouztchier pseudospectralmethodbasedonmuntzlegendrewaveletsforsolvingtheabelintegralequation AT fmotawfiq pseudospectralmethodbasedonmuntzlegendrewaveletsforsolvingtheabelintegralequation |