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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
Autor principal: Alzahrani, S S
Otros Autores: Alanazi, Abeer A, Atta Ahmed Gamal
Publicado:
MDPI AG
Materias:
Chebyshev approximation
Approximation
Numerical analysis
Diffusion waves
Methods
Mathematical analysis
Wave equations
Numerical methods
Sobolev space
Polynomials
Acceso en línea:Citation/Abstract
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Resumen: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.
ISSN:2073-8994
DOI:10.3390/sym17091451
Fuente:Engineering Database