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Collocation Method for the Time-Fractional Generalized Kawahara Equation Using a Certain Lucas Polynomial Sequence

Tallennettuna:
Julkaisussa:Axioms vol. 14, no. 2 (2025), p. 114
Päätekijä: Waleed Mohamed Abd-Elhameed
Muut tekijät: Abdulrahman Khalid Al-Harbi, Omar Mazen Alqubori, Alharbi, Mohammed H, Ahmed Gamal Atta
Julkaistu:
MDPI AG
Aiheet:
Basis functions
Numerical analysis
Algorithms
Error analysis
Methods
Partial differential equations
Polynomials
Differential equations
Collocation methods
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Abstrakti:This paper proposes a numerical technique to solve the time-fractional generalized Kawahara differential equation (TFGKDE). Certain shifted Lucas polynomials are utilized as basis functions. We first establish some new formulas concerned with the introduced polynomials and then tackle the equation using a suitable collocation procedure. The integer and fractional derivatives of the shifted polynomials are used with the typical collocation method to convert the equation with its governing conditions into a system of algebraic equations. The convergence and error analysis of the proposed double expansion are rigorously investigated, demonstrating its accuracy and efficiency. Illustrative examples are provided to validate the effectiveness and applicability of the proposed algorithm.
ISSN:2075-1680
DOI:10.3390/axioms14020114
Lähde:Engineering Database