Numerical Treatment of the Time Fractional Diffusion Wave Problem Using Chebyshev Polynomials
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| Publicado en: | Symmetry vol. 17, no. 9 (2025), p. 1451-1470 |
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MDPI AG
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| Acceso en línea: | Citation/Abstract Full Text + Graphics Full Text - PDF |
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| 024 | 7 | |a 10.3390/sym17091451 |2 doi | |
| 035 | |a 3254649208 | ||
| 045 | 2 | |b d20250101 |b d20251231 | |
| 084 | |a 231635 |2 nlm | ||
| 100 | 1 | |a Alzahrani, S S |u Department of Mathematics, College of Science, Taibah University, Madinah P.O. Box 344, Saudi Arabia | |
| 245 | 1 | |a Numerical Treatment of the Time Fractional Diffusion Wave Problem Using Chebyshev Polynomials | |
| 260 | |b MDPI AG |c 2025 | ||
| 513 | |a Journal Article | ||
| 520 | 3 | |a This paper introduces an efficient numerical method based on applying the typical Petrov–Galerkin approach (<inline-formula>PGA</inline-formula>) to solve the time fractional diffusion wave equation (<inline-formula>TFDWE</inline-formula>). The method utilises asymmetric polynomials, namely, shifted second-kind Chebyshev polynomials (<inline-formula>SSKCPs</inline-formula>). New derivative formulas are derived and used for these polynomials to establish the operational matrices of their derivatives. The paper presents rigorous error bounds for the proposed method in Chebyshev-weighted Sobolev space and demonstrates its accuracy and efficiency through several illustrative numerical examples. The results reveal that the method achieves high accuracy with relatively low polynomial degrees. | |
| 653 | |a Chebyshev approximation | ||
| 653 | |a Approximation | ||
| 653 | |a Numerical analysis | ||
| 653 | |a Diffusion waves | ||
| 653 | |a Methods | ||
| 653 | |a Mathematical analysis | ||
| 653 | |a Wave equations | ||
| 653 | |a Numerical methods | ||
| 653 | |a Sobolev space | ||
| 653 | |a Polynomials | ||
| 700 | 1 | |a Alanazi, Abeer A |u Department of Mathematics, College of Science, Taibah University, Madinah P.O. Box 344, Saudi Arabia | |
| 700 | 1 | |a Atta Ahmed Gamal |u Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo 11341, Egypt | |
| 773 | 0 | |t Symmetry |g vol. 17, no. 9 (2025), p. 1451-1470 | |
| 786 | 0 | |d ProQuest |t Engineering Database | |
| 856 | 4 | 1 | |3 Citation/Abstract |u https://www.proquest.com/docview/3254649208/abstract/embedded/7BTGNMKEMPT1V9Z2?source=fedsrch |
| 856 | 4 | 0 | |3 Full Text + Graphics |u https://www.proquest.com/docview/3254649208/fulltextwithgraphics/embedded/7BTGNMKEMPT1V9Z2?source=fedsrch |
| 856 | 4 | 0 | |3 Full Text - PDF |u https://www.proquest.com/docview/3254649208/fulltextPDF/embedded/7BTGNMKEMPT1V9Z2?source=fedsrch |