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

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I whakaputaina i:	Axioms vol. 14, no. 2 (2025), p. 114
Kaituhi matua:	Waleed Mohamed Abd-Elhameed
Ētahi atu kaituhi:	Abdulrahman Khalid Al-Harbi, Omar Mazen Alqubori, Alharbi, Mohammed H, Ahmed Gamal Atta
I whakaputaina:	MDPI AG
Ngā marau:	Basis functions Numerical analysis Algorithms Error analysis Methods Partial differential equations Polynomials Differential equations Collocation methods
Urunga tuihono:	Citation/Abstract Full Text + Graphics Full Text - PDF
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Whakaahuatanga
Whakarāpopotonga:	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
Puna:	Engineering Database