Numerical Treatment of the Time-Fractional Kuramoto–Sivashinsky Equation Using a Combined Chebyshev-Collocation Approach

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Detalles Bibliográficos
Publicado en:	Fractal and Fractional vol. 9, no. 11 (2025), p. 727-750
Autor principal:	Abd-Elhameed, Waleed Mohamed
Otros Autores:	Abdelkawy, Mohamed A, Alsafri Naher Mohammed A., Atta Ahmed Gamal
Publicado:	MDPI AG
Materias:	Applied mathematics Physics Partial differential equations Mathematical analysis Numerical analysis Polynomials Collocation methods Chebyshev approximation Approximation Algorithms Error analysis Methods
Acceso en línea:	Citation/Abstract Full Text + Graphics Full Text - PDF
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Descripción
Resumen:	In this paper, we present a collocation algorithm for numerically treating the time-fractional Kuramoto–Sivashinsky equation (TFKSE). Certain orthogonal polynomials, which are expressed as combinations of Chebyshev polynomials, and their shifted polynomials are introduced. Some new theoretical formulas regarding these polynomials have been developed, including their operational matrices of both integer and fractional derivatives. The derived formulas will be the foundation for designing the proposed numerical algorithm, which relies on converting the governing problem with its underlying conditions into a nonlinear algebraic system, which can be solved using Newton’s iteration technique. A rigorous error analysis for the proposed combined Chebyshev expansion is presented. Some numerical examples are given to ensure the applicability and efficiency of the presented algorithm. These results demonstrate that the proposed algorithm attains superior accuracy with fewer expansion terms.
ISSN:	2504-3110
DOI:	10.3390/fractalfract9110727
Fuente:	Engineering Database